Information transmission method and transmission device, and information reception method and reception device

ABSTRACT

In a wireless communication system, a transmission device generates (K+J) bits by adding J cyclic redundancy check (CRC) bits to K information bits, and interleaves the (K+J) bits according to a seed value-based interleaving pattern. The transmission device encodes the bits interleaved according to the interleaving pattern, using a polar code. The seed value permutates the CRC bits, and a value previously determined according to K is used as the seed value.

TECHNICAL FIELD

The present disclosure relates to a wireless communication system, andmore particularly to, a method and device for receiving/transmitting adownlink signal.

BACKGROUND ART

With appearance and spread of machine-to-machine (M2M) communication,machine type communication (MTC) and a variety of devices such assmartphones and tablet Personal Computers (PCs) and technology demandinga large amount of data transmission, data throughput needed in acellular network has rapidly increased. To satisfy such rapidlyincreasing data throughput, carrier aggregation technology, cognitiveradio technology, etc. for efficiently employing more frequency bandsand multiple input multiple output (MIMO) technology, multi-base station(BS) cooperation technology, etc. for raising data capacity transmittedon limited frequency resources have been developed.

As more communication devices have demanded higher communicationcapacity, there has been necessity of enhanced mobile broadband (eMBB)relative to legacy radio access technology (RAT). In addition, massivemachine type communication (mMTC) for providing various services anytimeand anywhere by connecting a plurality of devices and objects to eachother is one main issue to be considered in future-generationcommunication.

Further, a communication system to be designed in consideration ofservices/UEs sensitive to reliability and latency is under discussion.The introduction of future-generation RAT has been discussed by takinginto consideration eMBB communication, mMTC, ultra-reliable andlow-latency communication (URLLC), and the like.

DISCLOSURE Technical Problem

Due to introduction of new radio communication technology, the number ofuser equipments (UEs) to which a BS should provide a service in aprescribed resource region increases and the amount of data and controlinformation that the BS should transmit to the UEs increases. Since theamount of resources available to the BS for communication with the UE(s)is limited, a new method in which the BS efficiently receives/transmitsuplink/downlink data and/or uplink/downlink control information usingthe limited radio resources is needed. In other words, as the density ofnodes and/or the density of UEs increases, a method of efficiently usinghigh-density nodes or high-density UEs for communication is needed.

With development of technologies, overcoming delay or latency has becomean important challenge. Applications whose performance criticallydepends on delay/latency are increasing. Accordingly, a method to reducedelay/latency compared to the legacy system is demanded.

In a new communication system, the use of polar codes has beenconsidered to improve channel coding performance. Generally, the polarcode is much greater than other codes used for channel coding. Thus,considering a case in which the polar code is used for channel coding, amethod of improving the decoding speed of the polar code is required.

If a normal interleaver is applied to bits obtained using the polarcode, latency may increase. Thus, an interleaver for improving the speedof decoding when the polar code is used is required.

The technical objects that can be achieved through the presentdisclosure are not limited to what has been particularly describedhereinabove and other technical objects not described herein will bemore clearly understood by persons skilled in the art from the followingdetailed description.

Technical Solution

In an aspect of the present disclosure, provided herein is a method oftransmitting information by a transmitting device in a wirelesscommunication system. The method may include: generating K+J bits byadding J cyclic redundancy check (CRC) bits to K information bits;interleaving the K+J bits according to an interleaving pattern based ona seed value for permuting the J CRC bits; encoding the interleaved bitsbased on a polar code; and transmitting the encoded bits to a receivingdevice. The seed value may be predetermined based on K.

In another aspect of the present disclosure, provided herein is atransmitting device for transmitting information in a wirelesscommunication system. The transmitting device may include: a CRC encoderconfigured to generate K+J bits by adding J CRC bits to K informationbits; an interleaver configured to interleave the K+J bits according toan interleaving pattern based on a seed value for permuting the J CRCbits; a polar encoder configured to encode the interleaved bits based ona polar code; and a transceiver configured to transmit the encoded bitsto a receiving device. The seed value may be predetermined based on K.

In still another aspect of the present disclosure, provided herein is amethod of receiving information by a receiving device in a wirelesscommunication system. The method may include: receiving, from atransmitting device, K+J bits encoded based on a polar code, where K isthe number of information bits and J is the number of CRC bits; anddecoding the K+J bits based on the polar code according to aninterleaving pattern. The interleaving pattern may be based on a seedvalue for permuting the J CRC bits, and the seed value may bepredetermined based on K.

In a further aspect of the present disclosure, provided herein is areceiving device for receiving information in a wireless communicationsystem. The receiving device may include: a transceiver configured toreceive, from a transmitting device, K+J bits encoded based on a polarcode, where K is the number of information bits and J is the number ofCRC bits; and a polar decoder configured to decode the K+J bits based onthe polar code according to an interleaving pattern. The interleavingpattern may be based on a seed value for permuting the J CRC bits, andthe seed value may be predetermined based on K.

In each aspect of the present disclosure, when J=19 and a CRC generatorpolynomial for generation of the J CRC bits isx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1, a seed value forK+J=64 may be s=(5,8,4,15,7,19,18,16,6,14,10,12,13,9,11,2,1,3,17).

In each aspect of the present disclosure, an interleaving pattern forK+J=64 may be Int=(6, 7, 8, 10, 11, 16, 18, 19, 20, 23, 26, 27, 28, 30,32, 36, 39, 40, 43, 45, 50, 1, 4, 13, 14, 24, 34, 37, 44, 53, 2, 9, 29,42, 49, 5, 12, 15, 17, 21, 22, 25, 33, 38, 41, 60, 3, 35, 52, 31, 64,63, 61, 51, 59, 55, 57, 58, 54, 56, 47, 46, 48, 62).

In each aspect of the present disclosure, an interleaving pattern forK+J=64 may be Int=(6, 7, 8, 10, 11, 16, 18, 19, 20, 23, 26, 27, 28, 30,32, 36, 39, 40, 43, 45, 50, 1, 4, 13, 14, 24, 34, 37, 44, 53, 2, 9, 29,42, 49, 5, 12, 15, 17, 21, 22, 25, 33, 38, 41, 60, 3, 35, 52, 31, 46,47, 48, 51, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64).

In each aspect of the present disclosure, an interleaving pattern forK+J=K′ smaller than 64 may include values greater than 0 among valuesobtained by subtracting 64-K from each element of the interleavingpattern for K+J=64.

In each aspect of the present disclosure, when J=19 and a CRC generatorpolynomial for generation of the J CRC bits isx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1, a seed value forK+J=128 may be s=(11,10,1,12,13,17,19,2,6,4,14,16,5,3,15,8,18,7,9).

In each aspect of the present disclosure, when J=19 and a CRC generatorpolynomial for generation of the J CRC bits isx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1, a seed value forK+J=192 may be s=(3,6,1,5,8,19,10,2,15,4,12,11,9,17,16,13,14,7,18).

In each aspect of the present disclosure, when J=19 and a CRC generatorpolynomial for J CRC codes isx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1, a seed value forK+J=256 may be s=(6,3,11,19,9,15,12,14,8,1,10,2,17,7,13,5,18,4,16).

In each aspect of the present disclosure, when J=19 and a CRC generatorpolynomial for J CRC codes isx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1, a seed value forK+J=320 may be s=(3,6,11,13,2,8,18,4,1,12,5,7,14,17,10,15,16,19,9).

In each aspect of the present disclosure, when J=19 and a CRC generatorpolynomial for

J CRC codes is x¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1, aseed value for K+J=384 may bes=(6,3,11,5,1,8,2,9,17,19,15,13,14,12,18,4,10,16,7).

In each aspect of the present disclosure, when J=19 and a CRC generatorpolynomial for J CRC codes isx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1, a seed value forK+J=448 may be s=(6,3,18,2,1,16,10,19,8,17,9,13,5,7,4,12,14,11,15).

In each aspect of the present disclosure, when J=19 and a CRC generatorpolynomial for J CRC codes isx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1, a seed value forK+J=512 may be s=(3,6,11,2,5,12,16,8,10,1,13,17,9,19,18,7,14,15,4).

In each aspect of the present disclosure, when J=19 and a CRC generatorpolynomial for J CRC codes isx¹⁹+x¹⁸+x¹⁵+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1, a seed value forK+J=576 may be s=(6,11,9,7,10,13,16,2,8,15,4,1,3,17,19,12,5,14,18).

In each aspect of the present disclosure, when J=19 and a CRC generatorpolynomial for J CRC codes isx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1, a seed value forK+J=640 may be s=(1,2,19,8,18,16,17,13,4,12,3,7,9,6,10,5,15,11,14).

In each aspect of the present disclosure, when J=19 and a CRC generatorpolynomial for J CRC codes isx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1, a seed value forK+J=704 may be s=(19,1,18,15,16,17,6,11,2,12,9,5,7,13,4,14,10,8,3).

In each aspect of the present disclosure, when J=19 and a CRC generatorpolynomial for J CRC codes isx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1, a seed value forK+J=768 may be s=(2,1,3,12,5,4,18,15,7,16,14,13,17,8,6,19,10,9,11).

In each aspect of the present disclosure, when J=19 and a CRC generatorpolynomial for J CRC codes isx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1, a seed value forK+J>768 may be s=(1,6,9,12,13,8,10,19,14,4,16,5,3,2,15,7,11,17,18).

The above technical solutions are merely some parts of the examples ofthe present disclosure and various examples into which the technicalfeatures of the present disclosure are incorporated can be derived andunderstood by persons skilled in the art from the following detaileddescription of the present disclosure.

Advantageous Effects

According to example(s) of the present disclosure, uplink/downlinksignals can be efficiently transmitted/received. Therefore, overallthroughput of a radio communication system can be improved.

In addition, signals can be transmitted/received efficiently and at alow error rate in a wireless communication system.

According to the present disclosure, when a polar code is used forchannel coding, the speed of decoding may be improved.

It will be appreciated by persons skilled in the art that that theeffects that can be achieved through the present disclosure are notlimited to what has been particularly described hereinabove and otheradvantages of the present disclosure will be more clearly understoodfrom the following detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the disclosure, illustrate examples of the disclosureand together with the description serve to explain the principle of thedisclosure.

FIG. 1 illustrates a transport block processing procedure in anLTE/LTE-A system.

FIG. 2 is a block diagram illustrating rate matching performed byseparating an encoded code block into a systematic part and a paritypart.

FIG. 3 illustrates an internal structure of a circular buffer.

FIG. 4 is a block diagram for a polar code encoder.

FIG. 5 illustrates the concept of channel combining and channelsplitting for channel polarization.

FIG. 6 illustrates N-th level channel combining for a polar code.

FIG. 7 illustrates an evolution of decoding paths in a list-L decodingprocess.

FIG. 8 illustrates the concept of selecting position(s) to whichinformation bit(s) are to be allocated in polar codes.

FIG. 9 illustrates puncturing and information bit allocation accordingto the present disclosure.

FIG. 10 illustrates the concepts of a conventional CRC code and adistributed CRC code.

FIG. 11 illustrates an encoding procedure based on a polar code using adistributed CRC scheme.

FIG. 12 is a block diagram illustrating elements of a transmittingdevice 10 and a receiving device 20 for implementing the presentdisclosure.

MODE FOR CARRYING OUT THE INVENTION

Reference will now be made in detail to the exemplary examples of thepresent disclosure, examples of which are illustrated in theaccompanying drawings. The detailed description, which will be givenbelow with reference to the accompanying drawings, is intended toexplain exemplary examples of the present disclosure, rather than toshow the only examples that can be implemented according to thedisclosure. The following detailed description includes specific detailsin order to provide a thorough understanding of the present disclosure.However, it will be apparent to those skilled in the art that thepresent disclosure may be practiced without such specific details.

In some instances, known structures and devices are omitted or are shownin block diagram form, focusing on important features of the structuresand devices, so as not to obscure the concept of the present disclosure.The same reference numbers will be used throughout this specification torefer to the same or like parts.

The following techniques, apparatuses, and systems may be applied to avariety of wireless multiple access systems. Examples of the multipleaccess systems include a code division multiple access (CDMA) system, afrequency division multiple access (FDMA) system, a time divisionmultiple access (TDMA) system, an orthogonal frequency division multipleaccess (OFDMA) system, a single carrier frequency division multipleaccess (SC-FDMA) system, and a multicarrier frequency division multipleaccess (MC-FDMA) system. CDMA may be embodied through radio technologysuch as universal terrestrial radio access (UTRA) or CDMA2000. TDMA maybe embodied through radio technology such as global system for mobilecommunications (GSM), general packet radio service (GPRS), or enhanceddata rates for GSM evolution (EDGE). OFDMA may be embodied through radiotechnology such as institute of electrical and electronics engineers(IEEE) 802.11 (Wi-Fi), IEEE 802.16 (WiMAX), IEEE 802.20, or evolved UTRA(E-UTRA). UTRA is a part of a universal mobile telecommunications system(UMTS). 3rd generation partnership project (3GPP) long term evolution(LTE) is a part of evolved UMTS (E-UMTS) using E-UTRA. 3GPP LTE employsOFDMA in DL and SC-FDMA in UL. LTE-advanced (LTE-A) is an evolvedversion of 3GPP LTE. For convenience of description, it is assumed thatthe present disclosure is applied to 3GPP based communication system,e.g. LTE/LTE-A, NR. However, the technical features of the presentdisclosure are not limited thereto. For example, although the followingdetailed description is given based on a mobile communication systemcorresponding to a 3GPP LTE/LTE-A/NR system, aspects of the presentdisclosure that are not specific to 3GPP LTE/LTE-A/NR are applicable toother mobile communication systems.

In examples of the present disclosure described below, the expressionthat “assumes” may mean that a subject which transmits a channeltransmits the channel in accordance with the corresponding “assumption”.This may also mean that a subject which receives the channel receives ordecodes the channel in a form conforming to the “assumption”, on theassumption that the channel has been transmitted according to the“assumption”.

In the present disclosure, a user equipment (UE) may be a fixed ormobile device. Examples of the UE include various devices that transmitand receive user data and/or various kinds of control information to andfrom a base station (BS). The UE may be referred to as a terminalequipment (TE), a mobile station (MS), a mobile terminal (MT), a userterminal (UT), a subscriber station (SS), a wireless device, a personaldigital assistant (PDA), a wireless modem, a handheld device, etc. Inaddition, in the present disclosure, a BS generally refers to a fixedstation that performs communication with a UE and/or another BS, andexchanges various kinds of data and control information with the UE andanother BS. The BS may be referred to as an advanced base station (ABS),a node-B (NB), an evolved node-B (eNB), a base transceiver system (BTS),an access point (AP), a processing server (PS), etc. Particularly, a BSof a UTRAN is referred to as a Node-B, a BS of an E-UTRAN is referred toas an eNB, and a BS of a new radio access technology network is referredto as an gNB. Herein, for convenience of description, a base stationwill be referred to as a BS irrespective of communication technologies.

In the present disclosure, a node refers to a fixed point capable oftransmitting/receiving a radio signal through communication with a UE.Various types of BSs may be used as nodes irrespective of the termsthereof. For example, a BS, a node B (NB), an e-node B (eNB), apico-cell eNB (PeNB), a home eNB (HeNB), a relay, a repeater, etc. maybe a node. In addition, the node may not be a BS. For example, the nodemay be a radio remote head (RRH) or a radio remote unit (RRU). The RRHor RRU generally has a lower power level than a power level of a BS.Since the RRH or RRU (hereinafter, RRH/RRU) is generally connected tothe BS through a dedicated line such as an optical cable, cooperativecommunication between RRH/RRU and the BS can be smoothly performed incomparison with cooperative communication between BSs connected by aradio line. At least one antenna is installed per node. The antenna maymean a physical antenna or mean an antenna port or a virtual antenna.

In the present disclosure, a cell refers to a prescribed geographicalarea to which one or more nodes provide a communication service.Accordingly, in the present disclosure, communicating with a specificcell may mean communicating with a BS or a node which provides acommunication service to the specific cell. In addition, a DL/UL signalof a specific cell refers to a DL/UL signal from/to a BS or a node whichprovides a communication service to the specific cell. A node providingUL/DL communication services to a UE is called a serving node and a cellto which UL/DL communication services are provided by the serving nodeis especially called a serving cell. Furthermore, channel status/qualityof a specific cell refers to channel status/quality of a channel orcommunication link formed between a BS or node which provides acommunication service to the specific cell and a UE. In the 3GPP basedcommunication system, the UE may measure DL channel state received froma specific node using cell-specific reference signal(s) (CRS(s))transmitted on a CRS resource and/or channel state information referencesignal(s) (CSI-RS(s)) transmitted on a CSI-RS resource, allocated byantenna port(s) of the specific node to the specific node.

Meanwhile, a 3GPP based communication system uses the concept of a cellin order to manage radio resources and a cell associated with the radioresources is distinguished from a cell of a geographic region.

A “cell” of a geographic region may be understood as coverage withinwhich a node can provide service using a carrier and a “cell” of a radioresource is associated with bandwidth (BW) which is a frequency rangeconfigured by the carrier. Since DL coverage, which is a range withinwhich the node is capable of transmitting a valid signal, and ULcoverage, which is a range within which the node is capable of receivingthe valid signal from the UE, depends upon a carrier carrying thesignal, the coverage of the node may be associated with coverage of the“cell” of a radio resource used by the node. Accordingly, the term“cell” may be used to indicate service coverage of the node sometimes, aradio resource at other times, or a range that a signal using a radioresource can reach with valid strength at other times.

Meanwhile, the 3GPP communication standards use the concept of a cell tomanage radio resources. The “cell” associated with the radio resourcesis defined by combination of downlink resources and uplink resources,that is, combination of DL CC and UL CC. The cell may be configured bydownlink resources only, or may be configured by downlink resources anduplink resources. If carrier aggregation is supported, linkage between acarrier frequency of the downlink resources (or DL CC) and a carrierfrequency of the uplink resources (or UL CC) may be indicated by systeminformation. For example, combination of the DL resources and the ULresources may be indicated by linkage of system information block type 2(SIB2). The carrier frequency may be the same as a center frequency ofeach cell or CC. A cell operating on a primary frequency may be referredto as a primary cell (Pcell) or PCC, and a cell operating on a secondaryfrequency may be referred to as a secondary cell (Scell) or SCC. Thecarrier corresponding to the Pcell on downlink will be referred to as adownlink primary CC (DL PCC), and the carrier corresponding to the Pcellon uplink will be referred to as an uplink primary CC (UL PCC). A Scellmeans a cell that may be configured after completion of radio resourcecontrol (RRC) connection establishment and used to provide additionalradio resources. The Scell may form a set of serving cells for the UEtogether with the Pcell in accordance with capabilities of the UE. Thecarrier corresponding to the Scell on the downlink will be referred toas downlink secondary CC (DL SCC), and the carrier corresponding to theScell on the uplink will be referred to as uplink secondary CC (UL SCC).Although the UE is in RRC-CONNECTED state, if it is not configured bycarrier aggregation or does not support carrier aggregation, a singleserving cell configured by the Pcell only exists.

3GPP based communication standards define DL physical channelscorresponding to resource elements carrying information derived from ahigher layer and DL physical signals corresponding to resource elementswhich are used by a physical layer but which do not carry informationderived from a higher layer. For example, a physical downlink sharedchannel (PDSCH), a physical broadcast channel (PBCH), a physicalmulticast channel (PMCH), a physical control format indicator channel(PCFICH), a physical downlink control channel (PDCCH), and a physicalhybrid ARQ indicator channel (PHICH) are defined as the DL physicalchannels, and a reference signal and a synchronization signal aredefined as the DL physical signals. A reference signal (RS), also calleda pilot, refers to a special waveform of a predefined signal known toboth a BS and a UE. For example, a cell-specific RS (CRS), a UE-specificRS (UE-RS), a positioning RS (PRS), and channel state information RS(CSI-RS) may be defined as DL RSs. Meanwhile, the 3GPP basedcommunication standards define UL physical channels corresponding toresource elements carrying information derived from a higher layer andUL physical signals corresponding to resource elements which are used bya physical layer but which do not carry information derived from ahigher layer. For example, a physical uplink shared channel (PUSCH), aphysical uplink control channel (PUCCH), and a physical random accesschannel (PRACH) are defined as the UL physical channels, and ademodulation reference signal (DM RS) for a UL control/data signal and asounding reference signal (SRS) used for UL channel measurement aredefined as the UL physical signals.

In the present disclosure, a physical downlink control channel (PDCCH),a physical control format indicator channel (PCFICH), a physical hybridautomatic retransmit request indicator channel (PHICH), and a physicaldownlink shared channel (PDSCH) refer to a set of time-frequencyresources or resource elements (REs) carrying downlink controlinformation (DCI), a set of time-frequency resources or REs carrying acontrol format indicator (CFI), a set of time-frequency resources or REscarrying downlink acknowledgement (ACK)/negative ACK (NACK), and a setof time-frequency resources or REs carrying downlink data, respectively.In addition, a physical uplink control channel (PUCCH), a physicaluplink shared channel (PUSCH) and a physical random access channel(PRACH) refer to a set of time-frequency resources or REs carryinguplink control information (UCI), a set of time-frequency resources orREs carrying uplink data and a set of time-frequency resources or REscarrying random access signals, respectively. In the present disclosure,in particular, a time-frequency resource or RE that is assigned to orbelongs to PDCCH/PCFICH/PHICH/PDSCH/PUCCH/PUSCH/PRACH is referred to asPDCCH/PCFICH/PHICH/PDSCH/PUCCH/PUSCH/PRACH RE orPDCCH/PCFICH/PHICH/PDSCH/PUCCH/PUSCH/PRACH time-frequency resource,respectively. Therefore, in the present disclosure, PUCCH/PUSCH/PRACHtransmission of a UE is conceptually identical to UCI/uplink data/randomaccess signal transmission on PUSCH/PUCCH/PRACH, respectively. Inaddition, PDCCH/PCFICH/PHICH/PDSCH transmission of a BS is conceptuallyidentical to downlink data/DCI transmission on PDCCH/PCFICH/PHICH/PDSCH,respectively.

For terms and technologies which are not described in detail in thepresent disclosure, reference can be made to the standard document of3GPP LTE/LTE-A, for example, 3GPP TS 36.211, 3GPP TS 36.212, 3GPP TS36.213, 3GPP TS 36.321, and 3GPP TS 36.331 and the standard document of3GPP NR, for example, 3GPP TS 38.211, 3GPP TS 38.212, 3GPP TS 38.213,3GPP TS 38.214, 3GPP TS 38.300 and 3GPP TS 38.331. In addition, as topolar codes and the principle of encoding and decoding using the polarcodes, reference may be made to ‘E. Arikan, “Channel Polarization: AMethod for Constructing Capacity-Achieving Codes for SymmetricBinary-Input Memoryless Channels,” in IEEE Transactions on InformationTheory, vol. 55, no. 7, pp. 3051-3073, July 2009’.

As more communication devices have demanded higher communicationcapacity, there has been necessity of enhanced mobile broadband relativeto legacy radio access technology (RAT). In addition, massive machinetype communication for providing various services irrespective of timeand place by connecting a plurality of devices and objects to each otheris one main issue to be considered in future-generation communication.Further, a communication system design in which services/UEs sensitiveto reliability and latency are considered is under discussion. Theintroduction of future-generation RAT has been discussed by taking intoconsideration enhanced mobile broadband communication, massive MTC,ultra-reliable and low-latency communication (URLLC), and the like. Incurrent 3GPP, a study of the future-generation mobile communicationsystem after EPC is being conducted. In the present disclosure, thecorresponding technology is referred to as a new RAT (NR) or 5G RAT, forconvenience.

An NR communication system demands that much better performance than alegacy fourth generation (4G) system be supported in terms of data rate,capacity, latency, energy consumption, and cost. Accordingly, the NRsystem needs to make progress in terms of bandwidth, spectrum, energy,signaling efficiency, and cost per bit. NR needs to use efficientwaveforms in order to satisfy these requirements.

FIG. 1 illustrates a transport block processing procedure in anLTE/LTE-A system.

In order for a receiving side to correct errors that signals experiencein a channel, a transmitting side encodes information using a forwarderror correction code and then transmits the encoded information. Thereceiving side demodulates a received signal and decodes the errorcorrection code to thereby recover the information transmitted by thetransmitting side. In this decoding procedure, errors in the receivedsignal caused by a channel are corrected.

Data arrives at a coding block in the form of a maximum of two transportblocks every transmission time interval (TTI) in each DL/UL cell. Thefollowing coding steps may be applied to each transport block of theDL/UL cell:

-   -   cyclic redundancy check (CRC) attachment to a transport block;    -   code block segmentation and CRC attachment to a code block;    -   channel coding;    -   rate matching; and    -   code block concatenation.

Although various types of error correction codes are available, a turbocode has mainly been used in a legacy LTE/LTE-A system. The turbo codeis implemented by a recursive systematic convolution encoder and aninterleaver. For actual implementation of the turbo code, an interleaveris used to facilitate parallel decoding and quadratic polynomialpermutation (QPP) is a kind of interleaving. It is known that a QPPinterleaver maintains good performance only for a data block of aspecific size. It is known that performance of the turbo code increaseswith a larger data block size. In an actual communication system, a datablock of a predetermined size or larger is divided into a plurality ofsmaller data blocks and then is encoded, to facilitate actualimplementation of coding. The smaller data blocks are called codeblocks. While the code blocks are generally of the same size, one of thecode blocks may have a different size due to a limited size of the QPPinterleaver. Error correction coding is performed on each code block ofa predetermined interleaver size and then interleaving is performed toreduce the impact of burst errors that are generated during transmissionover a radio channel. The error-corrected and interleaved code block istransmitted by being mapped to an actual radio resource. The amount ofradio resources used for actual transmission is designated. Thus, theencoded code blocks are rate-matched to the amount of the radioresources. In general, rate matching is performed through puncturing orrepetition. For example, if the amount of radio resources, i.e., thenumber of transmission bits capable of being transmitted on the radioresources, is M and if a coded bit sequence, i.e., the number of outputbits of the encoder, is N, in which M is different from N, then ratematching is performed to match the length of the coded bit sequence toM. If M>N, then all or a part of bits of the coded bit sequence arerepeated to match the length of the rate-matched sequence to M. If M<N,then a part of the bits of the coded bit sequence is punctured to matchthe length of the rate-matched sequence to M and the punctured bits areexcluded from transmission.

Namely, in an LTE/LTE-A system, after data to be transmitted is encodedusing channel coding having a specific code rate (e.g., ⅓), the coderate of the data to be transmitted is adjusted through a rate-matchingprocedure consisting of puncturing and repetition. When the turbo codeis used as a channel code in the LTE/LTE-A system, a procedure ofperforming channel coding and rate-matching on each code block in thetransport block processing procedure as illustrated in FIG. 1 isillustrated in FIG. 2.

FIG. 2 is a block diagram illustrating rate matching performed byseparating an encoded code block into a systematic part and a paritypart.

As illustrated in FIG. 2, the mother code rate of an LTE/LTE-A turboencoder is ⅓. In order to obtain other code rates, if necessary,repetition or puncturing has to be performed, which are performed by arate matching module. The rate matching module consists of threeso-called sub-block interleavers for three output streams of the turboencoder and a bit selection and pruning part, which is realized by acircular buffer. The sub-block interleaver is based on a classicrow-column interleaver with 32 rows and length-32 intra-columnpermutation. The bits of each of the three streams are writtenrow-by-row into a matrix with 32 columns (number of rows depends onstream size). Dummy bits are padded to the front of each stream tocompletely fill the matrix. After column permutation, bits are read outfrom the matrix column-by-column.

FIG. 3 illustrates an internal structure of a circular buffer.

The circular buffer is the most important part of the rate matchingmodule, making it possible to perform puncturing and repetition of amother code. Referring to FIG. 2, the interleaved systematic bits arewritten into the circular buffer in sequence, with the first bit of theinterleaved systematic bit stream at the beginning of the buffer. Theinterleaved and interlaced parity bit streams are written into thebuffer in sequence, with the first bit of the stream next to the lastbit of the interleaved systematic bit stream. Coded bits (depending oncode rate) are read out serially from a certain starting point specifiedby redundancy version (RV) points in the circular buffer. If the codedbits reaches the end of the circular buffer and more coded bits areneeded for transmission (in the case of a code rate smaller than ⅓), atransmitting device wraps around and continues at the beginning of thecircular buffer.

HARQ, which stands for Hybrid ARQ, is an error correction mechanismbased on retransmission of packets, which are detected with errors. Thetransmitted packet arrives at a receiving device after a certainpropagation delay. The receiving device produces ACK for the case oferror-free transmission or NACK for the case of detection of someerrors. ACK/NACK is produced after some processing time and sent back tothe transmitting device and arrives at the transmitting device after apropagation delay. In the case of NACK, after a certain processing delayin the transmitting device, a desired packet will be sent again. Bits,which are read out from the circular buffer and sent throughretransmission, are different and depend on the position of the RV.There are four RVs (0, 1, 2, and 3), which define the position of astarting point at which the bits are read out from the circular buffer.Referring to FIG. 3, with the progressing number of retransmissions, theRV becomes higher and therefore fewer systematic bits and more paritybits are read out from the circular buffer for retransmission.

NR provides higher speeds and better coverage than current 4G. NRoperates in a high frequency band and is required to offer speeds of upto 1 Gb/s for tens of connections or tens of Mb/s for tens of thousandsof connections. To meet requirements of such an NR system, introductionof a more evolved coding scheme than a legacy coding scheme is underdiscussion. Since data communication arises in an incomplete channelenvironment, channel coding plays an important role in achieving ahigher data rate for fast and error-free communication. A selectedchannel code needs to provide superior block error ratio (BLER)performance for block lengths and code rates of a specific range.Herein, BLER is defined as the ratio of the number of erroneous receivedblocks to the total number of sent blocks. In NR, low calculationcomplexity, low latency, low cost, and higher flexibility are demandedfor a coding scheme. Furthermore, reduced energy per bit and improvedregion efficiency are needed to support a higher data rate. Use examplesfor NR networks are enhanced mobile broadband (eMBB), massive Internetof things (IoT), and ultra-reliable and low latency communication(URLLC). eMBB covers Internet access with high data rates to enable richmedia applications, cloud storage and applications, and augmentedreality for entertainment. Massive IoT applications include dense sensornetworks for smart homes/buildings, remote health monitoring, andlogistics tracking. URLLC covers critical applications that demandultra-high reliability and low latency, such as industrial automation,driverless vehicles, remote surgery, and smart grids.

Although many coding schemes with high capacity performance at largeblock lengths are available, many of these coding schemes do notconsistently exhibit excellent good performance in a wide range of blocklengths and code rates. However, turbo codes, low-density parity check(LPDC) codes, and polar codes show promising BLER performance in a widerange of coding rates and code lengths and hence are considered to beused in the NR system. As demand for various cases such as eMBB, massiveIoT, and URLLC has increased, a coding scheme providing greater channelcoding efficiency than in turbo codes is needed. In addition, increasein a maximum number of subscribers capable of being accommodated by achannel, i.e., increase in capacity, has been required.

Polar codes are codes providing a new framework capable of solvingproblems of legacy channel codes and were invented by Arikan at BilkentUniversity (reference: E. Arikan, “Channel Polarization: A Method forConstructing Capacity-Achieving Codes for Symmetric Binary-InputMemoryless Channels,” in IEEE Transactions on Information Theory, vol.55, no. 7, pp. 3051-3073, July 2009). Polar codes are the firstcapacity-achieving codes with low encoding and decoding complexities,which were proven mathematically. Polar codes outperform the turbo codesin large block lengths while no error flow is present. Hereinafter,channel coding using the polar codes is referred to as polar coding.

Polar codes are known as codes capable of achieving the capacity of agiven binary discrete memoryless channel. This can be achieved only whena block size is sufficiently large. That is, polar codes are codescapable of achieving the capacity of a channel if the size N of thecodes infinitely increases. Polar codes have low encoding and decodingcomplexity and may be successfully decoded. Polar codes are a sort oflinear block error correction codes. Multiple recursive concatenationsare basic building blocks for the polar codes and are bases for codeconstruction. Physical conversion of channels in which physical channelsare converted into virtual channels occurs and such conversion is basedon a plurality of recursive concatenations. If multiple channels aremultiplied and accumulated, most of the channels may become better orworse. The idea underlying polar codes is to use good channels. Forexample, data is sent through good channels at rate 1 and data is sentthrough bad channels at rate 0. That is, through channel polarization,channels enter a polarized state from a normal state.

FIG. 4 is a block diagram for a polar code encoder.

FIG. 4(a) illustrates a base module of a polar code, particularly, firstlevel channel combining for polar coding. In FIG. 4(a), W₂ denotes anentire equivalent channel obtained by combining two binary-inputdiscrete memoryless channels (B-DMCs), Ws. Herein, u₁ and u₂ arebinary-input source bits and y₁ and y₂ are output coded bits. Channelcombining is a procedure of concatenating the B-DMCs in parallel.

FIG. 4(b) illustrates a base matrix F for the base module. Thebinary-input source bits u₁ and u₂ input to the base matrix F and theoutput coded bits x₁ and x₂ of the base matrix F have the followingrelationship.

$\begin{matrix}{{\left\lbrack {u_{1}u_{2}} \right\rbrack \begin{bmatrix}1 & 0 \\1 & 1\end{bmatrix}} = \left\lbrack {x_{1}x_{2}} \right\rbrack} & {{Equation}\mspace{14mu} 1}\end{matrix}$

The channel W₂ may achieve symmetric capacity I(W) which is a highestrate. In the B-DMC W, symmetric capacity is an important parameter whichis used to measure a rate and is a highest rate at which reliablecommunication can occur over the channel W. The B-DMC may be defined asfollows.

$\begin{matrix}{{I(W)} = {\sum\limits_{y \in Y}{\sum\limits_{x \in X}{1\text{/}2{W\left( y \middle| x \right)}\log \frac{w\left( {yx} \right)}{{1\text{/}2{w\left( y \middle| 0 \right)}} + {1\text{/}2{w\left( y \middle| 1 \right)}}}}}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

It is possible to synthesize or create a second set of N binary inputchannels out of N independent copies of a given B-DMC W and the channelshave the properties {W_(N) ^((i)): 1≤i≤N}. If N increases, there is atendency for a part of the channels to have capacity approximating to 1and for the remaining channels to have capacity approximating to 0. Thisis called channel polarization. In other words, channel polarization isa process of creating a second set of N channels {W_(N) ^((i)): 1≤i≤N}using N independent copies of a given B-DMC W. The effect of channelpolarization means that, when N increases, all symmetric capacity terms{I(W_(N) ^((i)))} tend towards 0 or 1 for all except a vanishingfraction of indexes i. In other words, the concept behind channelpolarization in the polar codes is transforming N copies (i.e., Ntransmissions) of a channel having a symmetric capacity of I(W) (e.g.,additive white Gaussian noise channel) into extreme channels of capacityclose to 1 or 0. Among the N channels, an I(W) fraction will be perfectchannels and an 1−I(W) fraction will be completely noise channels. Then,information bits are transmitted only through good channels and bitsinput to the other channels are frozen to 1 or 0. The amount of channelpolarization increases along with a block length. Channel polarizationconsists of two phases: channel combining phase and channel splittingphase.

FIG. 5 illustrates the concept of channel combining and channelsplitting for channel polarization. As illustrated in FIG. 5, when Ncopies of an original channel W are properly combined to create a vectorchannel W_(vec) and then are split into new polarized channels, the newpolarized channels are categorized into channels having capacity C(W)=1and channels having C(W)=0 if N is sufficiently large. In this case,since bits passing through the channels having the channel capacityC(W))=1 are transmitted without error, it is better to transmitinformation bits therethrough and, since bits passing through thechannels having capacity C(W)=0 cannot transport information, it isbetter to transport frozen bits, which are meaningless bits,therethrough.

Referring to FIG. 5, copies of a given B-DMC W are combined in arecursive manner to output a vector channel W_(vec) given byX_(N)→Y_(N), where N=2^(n) and n is an integer equal to or greater than0. Recursion always begins at the 0th level and W₁=W. If n is 1 (n=1),this means the first level of recursion in which two independent copiesof W₁ are combined. If the above two copies are combined, a channel W₂:X₂→Y₂ is obtained. A transitional probability of this new channel W₂ maybe represented by the following equation.

W ₂(y ₁ ,y ₂ |u ₁ ,u ₂)=W(y ₁ |u ₁ ⊕u ₂)W(y ₁ |u ₂)   Equation 3

If the channel W₂ is obtained, two copies of the channel W₂ are combinedto obtain a single copy of a channel W₄. Such recursion may berepresented by W₄: X₄→Y₄ having the following transitional probability.

W ₄(y ₁ ⁴ |u ₁ ⁴)=W ₂(y ₁ ² |u ₁ ⊕u ₂ ,u ₃ ⊕u ₄)W ₂(y ₃ ⁴ |u ₂ ,u ₄)  Equation 4

In FIG. 5, G_(N) is a size-N generator matrix. G₂ corresponds to thebase matrix F illustrated in FIG. 4(b). G₄ may be represented by thefollowing matrix.

$\begin{matrix}{G_{4} = {{{\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & 1\end{bmatrix}\begin{bmatrix}1 & 0 \\1 & 1\end{bmatrix}} \otimes 2} = \begin{bmatrix}1 & 0 & 0 & 0 \\1 & 0 & 1 & 0 \\1 & 1 & 0 & 0 \\1 & 1 & 1 & 1\end{bmatrix}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

Herein, ⊗ denotes the Kronecker product, A^(⊗n)=A⊗A^(⊗(n−1)) for alln≥1, A^(⊗0)=1.

The relationship between input u^(N) ₁ to G_(N) and output x^(N) ₁ ofG_(N) of FIG. 5(b) may be represented as x^(N) ₁=u^(N) ₁G_(N), wherex^(N) ₁={x₁, . . . , x_(N)}, u^(N) ₁={u₁, . . . , u_(N)}

When N B-DMCs are combined, each B-DMC may be expressed in a recursivemanner. That is, G_(N) may be indicated by the following equation.

G_(N)=B_(N)F^(Wn)   Equation 6

Herein, N=2^(n), n≥1, F^(⊗n)=F⊗F^(⊗(n−1)), and F^(⊗0)=1. B_(N) is apermutation matrix known as a bit-reversal operation andB_(N)=R_(N)(I₂⊗B_(N/2)) and may be recursively computed. I₂ is a2-dimensional identity matrix and this recursion is initialized toB₂=I₂. R_(N) is a bit-reversal interleaver and is used to map an inputs^(N) ₁={s₁, . . . s_(N)} to an output x^(N) ₁={s₁, s₃, . . . , s_(N-1),s₂, . . . , s_(N)}. The bit-reversal interleaver may not be included ina transmitting side. The relationship of Equation is illustrated in FIG.6.

FIG. 6 illustrates N-th level channel combining for a polar code.

A process of defining an equivalent channel for specific input aftercombining N B-DMCs Ws is called channel splitting. Channel splitting maybe represented as a channel transition probability indicated by thefollowing equation.

$\begin{matrix}{{W_{N}^{i}\left( {y_{1}^{N},\left. u_{1}^{i - 1} \middle| u_{i} \right.} \right)} = {\sum_{u_{i + 1}^{N}}{\frac{1}{2^{N - 1}}{W_{N}\left( y_{1}^{N} \middle| u_{1}^{N} \right)}}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

Channel polarization has the following characteristics:

>Conservation: C(W⁻)+C(W⁺)=2C(W),

>Extremization: C(W⁻)≤C(W)≤C(W⁺).

When channel combining and channel splitting are performed, thefollowing theorem may be obtained.

* Theorem: For any B-DMC W, channels {W_(N) ^((i))} are polarized in thefollowing sense. For any fixed δ∈{0,1}, as N goes to infinity throughpowers of 2, the fraction of indexes i∈{1, . . . , N} for channelcapacity I(W_(N) ^((i)))∈(1−δ, 1] goes to I(W) and the faction of i forchannel capacity I(W_(N) ^((i)))∈[0,δ) goes to 1−I(W). Hence, if N→∞,then channels are perfectly noisy or are polarized free of noise. Thesechannels can be accurately recognized by the transmitting side.Therefore, bad channels are fixed and non-fixed bits may be transmittedon good channels.

That is, if the size N of polar codes is infinite, a channel has muchnoise or is free of noise, with respect to a specific input bit. Thishas the same meaning that the capacity of an equivalent channel for aspecific input bit is divided into 0 or I(W).

Inputs of a polar encoder are divided into bit channels to whichinformation data is mapped and bit channels to which the informationdata is not mapped. As described earlier, according to the theorem ofthe polar code, if a codeword of the polar code goes to infinity, theinput bit channels may be classified into noiseless channels and noisechannels. Therefore, if information is allocated to the noiseless bitchannels, channel capacity may be obtained. However, in actuality, acodeword of an infinite length cannot be configured, reliabilities ofthe input bit channels are calculated and data bits are allocated to theinput bit channels in order of reliabilities. In the present disclosure,bit channels to which data bits are allocated are referred to as goodbit channels. The good bit channels may be input bit channels to whichthe data bits are mapped. Bit channels to which data is not mapped arereferred to as frozen bit channels. A known value (e.g., 0) is input tothe frozen bit channels and then encoding is performed. Any values whichare known to the transmitting side and the receiving side may be mappedto the frozen bit channels. When puncturing or repetition is performed,information about the good bit channels may be used. For example,positions of codeword bits (i.e., output bits) corresponding topositions of input bits to which information bits are not allocated maybe punctured.

A decoding scheme of the polar codes is a successive cancellation (SC)decoding scheme. The SC decoding scheme obtains a channel transitionprobability and then calculates a likelihood ratio (LLR) of input bitsusing the channel transition probability. In this case, the channeltransition probability may be calculated in a recursive form if channelcombining and channel splitting procedures use characteristics of therecursive form. Therefore, a final LLR value may also be calculated inthe recursive form. First, a channel transition probability W_(N)^((i))(y₁ ^(N),u₁ ^(i−1)|u₁) of an input bit u₁ ^(i) may be obtained asfollows. u₁ ^(i) may be split into odd indexes and even indexes asexpressed as u_(1,o) ^(i), u_(1,e) ^(i), respectively. The channeltransition probability may be indicated by the following equations.

$\begin{matrix}{{\begin{matrix}{{W_{2N}^{({{2i} - 1})}\left( {y_{1}^{2N},\left. u_{1}^{{2i} - 1} \middle| u_{{2i} - 1} \right.} \right)} = {\sum_{u_{2\; i}^{2\; N}}{\frac{1}{2^{{2N} - 1}}{W_{2N}\left( y_{1}^{2N} \middle| u_{1}^{2N} \right)}}}} \\{= {\sum_{u_{{2\; i},o}^{2\; N},u_{{2\; i},e}^{2\; N}}{\frac{1}{2^{{2N} - 1}}W_{N}}}} \\{{\left( y_{1}^{N} \middle| {u_{1,o}^{2N} \oplus u_{i,e}^{2N}} \right){W_{N}\left( y_{N + 1}^{2N} \middle| u_{1,e}^{2N} \right)}}} \\{= {\sum_{u_{2\; i}}{\frac{1}{2}{\sum_{u_{{{2\; i} + 1},e}^{2\; N}}{\frac{1}{2^{N - 1}}W_{N}}}}}} \\{{\left( y_{N + 1}^{2N} \middle| u_{1,e}^{2N} \right) \cdot {\sum_{u_{{{2\; i} + 1},o}^{2\; N}}{\frac{1}{2^{N - 1}}W_{N}}}}} \\{\left( y_{1}^{N} \middle| {u_{1,o}^{2N} \oplus u_{i,e}^{2N}} \right)} \\{= {\sum_{u_{2\; i}}{\frac{1}{2}W_{N}^{(i)}}}} \\{{\left( {y_{1}^{N},{{u_{1,o}^{{2i} - 2} \oplus u_{i,e}^{{2i} - 2}}{u_{{2i} - 1} \oplus u_{2i}}}} \right)~ \cdot}} \\{{W_{N}^{(i)}\left( {y_{N + 1}^{2N},{u_{1,e}^{{2i} - 2}u_{2i}}} \right)}}\end{matrix}{where}\mspace{20mu} {W_{N}^{(i)}\left( {y_{1}^{N},{u_{1}^{i - 1}u_{i}}} \right)}}\mspace{11mu} = {\sum_{u_{i + 1}^{N}}{\frac{1}{2^{N - 1}}{{W_{N}\left( {y_{1}^{N}u_{1}^{N}} \right)}.}}}} & {{Equation}\mspace{14mu} 8} \\\begin{matrix}{{W_{2N}^{({2i})}\left( {y_{1}^{2N},\left. u_{1}^{{2i} - 1} \middle| u_{2i} \right.} \right)} = {\sum_{u_{{2\; i} + 1}^{2\; N}}{\frac{1}{2^{{2N} - 1}}{W_{2\; N}\left( y_{1}^{2N} \middle| u_{1}^{2N} \right)}}}} \\{= {\sum_{u_{{{2\; i} + 1},o}^{2\; N},u_{{{2\; i} + 1},e}^{2\; N}}{\frac{1}{2^{{2N} - 1}}W_{N}}}} \\{{\left( y_{1}^{N} \middle| {u_{1,o}^{2N} \oplus u_{i,e}^{2N}} \right){W_{N}\left( y_{N + 1}^{2N} \middle| u_{1,e}^{2N} \right)}}} \\{= {\frac{1}{2}{\sum_{u_{{{2\; i} + 1},e}^{2\; N}}{\frac{1}{2^{N - 1}}{{W_{N}\left( y_{N + 1}^{2N} \middle| u_{1,e}^{2N} \right)} \cdot}}}}} \\{{\sum_{u_{{{2\; i} + 1},o}^{2\; N}}{\frac{1}{2^{N - 1}}{W_{N}\left( {y_{1}^{N}{u_{1,o}^{2N} \oplus u_{i,e}^{2N}}} \right)}}}} \\{= {\frac{1}{2}{{W_{N}^{(i)}\left( {y_{1}^{N},{{u_{1,o}^{{2i} - 2} \oplus u_{i,e}^{{2i} - 2}}{u_{{2i} - 1} \oplus u_{2\; i}}}} \right)} \cdot}}} \\{{W_{N}^{(i)}\left( {y_{N + 1}^{2N},{u_{1,e}^{{2i} - 2}u_{2i}}} \right)}}\end{matrix} & {{Equation}\mspace{14mu} 9}\end{matrix}$

A polar decoder retrieves information and generates an estimateu{circumflex over ( )}^(N) ₁ of u^(N) ₁ using values (e.g., receptionbits, frozen bits, etc.) known for the polar codes. The LLR is definedas follows.

$\begin{matrix}{{L_{N}^{(i)}\left( {y_{1}^{N},u_{1}^{i - 1}} \right)} = \frac{W_{N}^{(i)}\left( {y_{1}^{N},{\left. u_{1}^{i - 1} \middle| u_{i} \right. = 0}} \right)}{W_{N}^{(i)}\left( {y_{1}^{N},{\left. u_{1}^{i - 1} \middle| u_{i} \right. = 1}} \right)}} & {{Equation}\mspace{14mu} 10}\end{matrix}$

The LLR may be recursively calculated as follows.

$\begin{matrix}{\mspace{79mu} {{{L_{N}^{({{2i} - 1})}\left( {y_{1}^{N},{\overset{\hat{}}{u}}_{1}^{{2i} - 2}} \right)} = \frac{\begin{matrix}{{L_{N/2}^{(i)}\left( {y_{1}^{N/2},{{\overset{\hat{}}{u}}_{1,o}^{{2i} - 2} \oplus {\hat{u}}_{1,e}^{{2i} - 2}}} \right)} \cdot} \\{{L_{N/2}^{(i)}\left( {y_{{N/2} + 1}^{N},{\overset{\hat{}}{u}}_{1,e}^{{2i} - 2}} \right)} + 1}\end{matrix}}{\begin{matrix}{{L_{N/2}^{(i)}\left( {y_{1}^{N/2},{{\overset{\hat{}}{u}}_{1,o}^{{2i} - 2} \oplus {\hat{u}}_{1,e}^{{2i} - 2}}} \right)} +} \\{L_{N/2}^{(i)}\left( {y_{{N/2} + 1}^{N},{\overset{\hat{}}{u}}_{1,e}^{{2i} - 2}} \right)}\end{matrix}}}{{L_{N}^{({2i})}\left( {y_{1}^{N},{\overset{\hat{}}{u}}_{1}^{{2i} - 2}} \right)} = {\left\lbrack {L_{N/2}^{(i)}\left( {y_{1}^{N/2},{{\overset{\hat{}}{u}}_{1,o}^{{2i} - 2} \oplus {\hat{u}}_{1,e}^{{2i} - 2}}} \right)} \right\rbrack^{1 - {2{\hat{u}}_{{2i} - 1}}} \cdot {L_{N/2}^{(i)}\left( {y_{{N/2} + 1}^{N},{\overset{\hat{}}{u}}_{1,e}^{{2i} - 2}} \right)}}}}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

Recursive calculation of LLRs is traced back to a code length of 1 withan LLR L⁽¹⁾ ₁(y₁)=W(y_(i)|0)/W(y_(i)|1). L⁽¹⁾ ₁(y_(i)) is softinformation observed from a channel.

The complexity of a polar encoder and an SC decoder varies with thelength N of polar codes and is known as having O(NlogN). Assuming that Kinput bits are used for a length-N polar code, a coding rate becomesN/K. If a generator matrix of a polar encoder of a data payload size Nis G_(N), an encoded bit may be represented as x^(N) ₁=u^(N) ₁G_(N). Itis assumed that K bits out of u^(N) ₁ correspond to payload bits, a rowindex of G_(N) corresponding to the payload bits is i, and a row indexof G_(N) corresponding to (N−K) bits is F. A minimum distance of thepolar codes may be given as d_(min)(C)=min_(i∈I)2^(wt(i)), where wt(i)is the number of is within binary extension of i and i=0, 1, . . . ,N−1.

SC list (SCL) decoding is an extension of a basic SC decoder. In thistype of decoder, L decoding paths are simultaneously considered in eachdecoding stage. Herein, L is an integer. In other words, in the case ofthe polar codes, a list-L decoding algorithm is an algorithm forsimultaneously tracking L paths in a decoding process.

FIG. 7 illustrates an evolution of decoding paths in a list-L decodingprocess. For convenience of description, it is assumed that the numberof bits that should be determined is n and all bits are not frozen. If alist size L is 4, each level includes at most 4 nodes with paths thatcontinue downward. Discontinued paths are expressed by dotted lines inFIG. 7. A process in which decoding paths evolve in list-L decoding willnow be described with reference to FIG. 7. i) If list-L decoding isstarted, the first unfrozen bit may be either 0 or 1. ii) list-Ldecoding continues. The second unfrozen bits may be either 0 or 1. Sincethe number of paths is not greater than L=4, pruning is not needed yet.iii) Consideration of all options for the first bit (i.e., a bit of thefirst level), the second bit (i.e. a bit of the second level), and thethird bit (i.e., a bit of the third level) results in 8 decoding pathswhich are excessive because L=4. iv) the 8 decoding paths are pruned toL (=4) promising paths. v) 4 active paths continue by considering twooptions of the fourth unfrozen bit. In this case, the number of paths isdoubled, i.e., 8 paths which are excessive because L=4. vi) The 8 pathsare pruned back to L (=4) best paths. In the example of FIG. 7, 4candidate codewords 0100, 0110, 0111, and 1111 are obtained and one ofthe codewords is determined to be a codeword most similar to an originalcodeword. In a similar manner to a normal decoding process, for example,in a pruning process or a process of determining a final codeword, apath in which the sum of LLR absolute values is largest may be selectedas a survival path. If a CRC is present, the survival path may beselected through the CRC.

Meanwhile, CRC-aided SCL decoding is SCL decoding using CRC and improvesthe performance of polar codes. CRC is the most widely used technique inerror detection and error correction in the field of information theoryand coding. For example, if an input block of an error correctionencoder has K bits and the length of information bits is k, and thelength of CRC sequences is m bits, then K=k+m. CRC bits are a part ofsource bits for an error correction code. If the size of channel codesused for encoding is N, a code rate R is defined as R=K/N. CRC aided SCLdecoding serves to detect an errorless path while a receiving deviceconfirms a CRC code with respect to each path. An SCL decoder outputscandidate sequences to a CRC detector. The CRC detector feeds back acheck result in order to aid in determining a codeword.

Although complicated as compared with an SC algorithm, SCL decoding orCRC aided SCL decoding has an advantage of excellent decodingperformance. For more details of a list-X decoding algorithm of thepolar codes, refer to ‘I. Tal and A. Vardy, “List decoding of polarcodes,” in Proc. IEEE Int. Symp. Inf. Theory, pp. 1-5, Jul. 2011’.

In the polar codes, code design is independent of a channel and hence isnot versatile for mobile fading channels. In addition, the polar codeshave a disadvantage of limited application because the codes haverecently been introduced and have not grown yet. That is, polar codingproposed up to now has many parts that have not been defined to apply toa wireless communication system. Therefore, the present disclosureproposes a polar coding method suitable for the wireless communicationsystem.

FIG. 8 illustrates the concept of selecting position(s) to whichinformation bit(s) are to be allocated in polar codes.

In FIG. 8, it is assumed that the size N of mother codes is 8, i.e., thesize N of polar codes is 8, and a code rate is ½.

In FIG. 8, C(W_(i)) denotes the capacity of a channel W, and correspondsto the reliability of channels that input bits of a polar codeexperience. When channel capacities corresponding to input bit positionsof the polar code are as illustrated in FIG. 8, reliabilities of theinput bit positions are ranked as illustrated in FIG. 8. To transmitdata at a code rate of ½, a transmitting device allocates 4 bitsconstituting the data to 4 input bit positions having high channelcapacities among 8 input bit positions (i.e., input bit positionsdenoted as U₄, U₆, U₇, and U₄ among input bit positions U₁ to U₈ of FIG.8) and freezes the other input bit positions. A generator matrix G₈corresponding to the polar code of FIG. 8 is as follows. The generatormatrix G₈ may be acquired based on Equation 6.

$\begin{matrix}{G_{8} = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 \\1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\end{bmatrix}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

The input bit positions denoted as U₁ to U₈ of FIG. 8 correspond one byone to rows from the lowest row to the highest row of G₈. Referring toFIG. 8, it may be appreciated that the input bit corresponding to U₈affects all output coded bits. On the other hand, it may be appreciatedthat the input bit corresponding to U₁ affects only Y₁ among the outputcoded bits. Referring to Equation 12, when binary-input source bits U₁to U₈ are multiplied by G₈, a row in which the input bits appear at alloutput bits is the lowest row [1, 1, 1, 1, 1, 1, 1, 1] in which allelements are 1, among rows of G₈. Meanwhile, a row in which thebinary-input source bits appears at only one output bit is a row inwhich one element is 1 among the rows of G₈, i.e., a row [1, 0, 0, 0, 0,0, 0, 0] in which a row weight is 1. Similarly, it may be appreciatedthat a row in which a row weight is 2 reflects input bits correspondingto the row in two output bits. Referring to FIG. 8 and Equation 12, U₁to U₈ correspond one by one to the rows of G₈ and bit indexes fordistinguishing between input positions of U₁ to U₈, i.e., bit indexesfor distinguishing between the input positions, may be assigned to therows of G₈.

Hereinafter, for Polar codes, it may be assumed that bit indexes from 0to N−1 are sequentially allocated to rows of G_(N) starting from thehighest row having the smallest row weight with respect to N input bits.For example, referring to FIG. 8, a bit index 0 is allocated to theinput position of U₁, i.e., the first row of G₈ and a bit index 7 isallocated to the input position of U₈, i.e., the last row of G₈.However, since the bit indexes are used to indicate input positions ofthe polar code, a scheme different from the above allocation scheme maybe used. For example, bit indexes from 0 to N−1 may be allocated staringfrom the lowest row having the largest row weight.

In the case of output bit indexes, as illustrated in FIG. 8 and Equation12, it may be assumed that bit indexes from 0 to N−1 or bit indexes from1 to N are assigned to columns from the first column having the largestcolumn weight to the last column having the smallest column weight amongcolumns of G_(N).

In Polar codes, setting of information bits and frozen bits is one ofthe most important elements in the configuration and performance of thepolar code. That is, determination of ranks of input bit positions maybe an important element in the performance and configuration of thepolar code. For Polar codes, bit indexes may distinguish input or outputpositions of the polar code. In the present disclosure, a sequenceobtained by enumerating reliabilities of bit positions in ascending ordescending order are referred to as a bit index sequence. That is, thebit index sequence represents reliabilities of input or output bitpositions of the polar code in ascending or descending order. Atransmitting device inputs information bits to input bits having highreliabilities based on the input bit index sequence and performsencoding using the polar code. A receiving device may discern inputpositions to which information bits are allocated or input positions towhich frozen bits are allocated, using the same or corresponding inputbit index sequence. That is, the receiving device may perform polardecoding using an input bit index sequence which is identical to orcorresponds to an input bit sequence used by the transmitting device andusing a corresponding polar code. In the following description, it maybe assumed that an input bit sequence is predetermined so thatinformation bit(s) may be allocated to input bit position(s) having highreliabilities.

FIG. 9 illustrates puncturing and information bit allocation for polarcodes. In FIG. 9, F denotes a frozen bit, D denotes an information bit,and 0 denotes a skipping bit.

Among coded bits, the case in which an information bit is changed to afrozen bit may occur according to an index or position of a puncturedbit. For example, if output coded bits for a mother code of N=8 shouldbe punctured in order of Y8, Y7, Y6, Y4, Y5, Y3, Y2, and Y1 and a targetcode rate is ½, then Y8, Y7, Y6, and Y4 are punctured, U8, U7, U6, andU4 connected only to Y8, Y7, Y6, and Y4 are frozen to 0, and these inputbits are not transmitted, as illustrated in FIG. 9. An input bit changedto a frozen bit by puncturing of a coded bit is referred to as askipping bit or a shortening bit and a corresponding input position isreferred to as a skipping position or a shortening position. Shorteningis a rate matching method of inserting a known bit into an input bitposition connected to a position of an output bit desired to betransmitted while maintaining the size of input information (i.e., thesize of information blocks). Shortening is possible starting from inputcorresponding to a column in which a column weight is 1 in a generatormatrix G_(N) and next shortening may be performed with respect to inputcorresponding to a column in which a column weight is 1 in a remainingmatrix from which a column and row in which a column weight is 1 areremoved. To prevent all information bits from being punctured, aninformation bit that should have been allocated to an information bitposition may be reallocated in order of a high reliability within a setof frozen bit positions.

In the case of the polar code, decoding may be generally performed inthe following order.

>1. Bit(s) having low reliabilities are recovered first. Althoughreliability differs according to the structure of a decoder, since aninput index in an encoder (hereinafter, an encoder input index) having alow value usually has a low reliability, decoding is generally performedstaring from a low encoder input index.

>2. When there is a known bit for a recovered bit, the known bit is usedtogether with the recovered bit or the process of 1 is omitted and aknown bit for a specific input bit position is immediately used, therebyrecovering an information bit, which is an unknown bit. The informationbit may be a source information bit (e.g., a bit of a transport block)or a CRC bit.

FIG. 10 illustrates the concepts of a conventional CRC code and adistributed CRC code. FIG. 10 (a) illustrates conventional CRC, and FIG.10 (b) illustrates distributed CRC.

In the polar code, a CRC-aided list (CAL) decoding method is widely useddue to superior decoding performance thereof. According to the CALdecoding method, L candidate information bit sequences, {u_(i): i−1, . .. , L} (where L is a positive integer) are first decoded. Then,CRC-CHECK is performed for the candidate information bit sequences, anda candidate sequence that passes CRC-CHECK is selected as a decodedinformation bit sequence.

In general, CRC bits are located after information bits as shown in FIG.10 (a). Thus, a decoder generally decodes all information bits and thenperforms CRC-CHECK for the decoded information bits. In recent years,distributed CRC has been proposed to improve the decoding speed of theCAL decoding method. In the distributed CRC, CRC bits are appropriatelydistributed over information bits as shown in FIG. 10 (b). When thedistributed CRC is used as shown in FIG. 10(a), a decoder may decodesome information bits (e.g., an information sub-block consisting of K₁bits) and some CRC bits (e.g., a CRC block consisting of J₁ bits) duringa CAL decoding process and perform CRC-CHECK for the decoded bits. Inthis case, if CRC-CHECK for all the L candidate information bitsequences fails, the decoder may declare an error and stop the decoding.That is, when the distributed CRC is used, early termination of decodingis enabled during the CAL decoding process. If decoding of a receivedsignal is capable of being terminated early, a receiving device canrapidly determine whether the received signal is for the correspondingreceiving device, whereby the receiving device may rapidly discover asignal therefor as well. Further, since an error in the received signalis rapidly detected, retransmission for the received signal or nexttransmission after the received signal may be rapidly performed as well.

However, to use the distributed CRC during a decoding process, it needsto be determined how CRC bits are distributed over information bits.Accordingly, the present disclosure proposes distributed CRC and a polardecoding method using the same to improve the decoding speed when thepolar code is used. In particular, the present disclosure proposes a bitinterleaver suitable for a distributed CRC scheme. In other words, thepresent disclosure provides a method of distributing CRC bits to achieveearly termination in CAL decoding.

FIG. 11 illustrates an encoding procedure based on a polar code using adistributed CRC scheme. Referring to FIG. 11, K information bits (i₁,i₂, . . . , i_(K)) are CRC-encoded into a CRC-encoded bit sequence witha size of K+J by a CRC encoder configured to add J CRC bits to theinformation bits. Generally, the CRC encoder is configured to add a CRCcode with a size of J to the end of the K information bits. The presentdisclosure is directed to a bit interleaver for changing the positionsof bits in the CRC-encoded bit sequence with the size of K+J. Inparticular, the present disclosure relates to design of the interleaverblock shown in FIG. 11. For example, assuming that K=10 and J=4 in FIG.11, if no interleaver is used in FIG. 11, an input of“i₁,i₂,i₃,i₄,i₅,i₆,i₇,i₈,i₉,i₁₀,p₁,p₂,p₃,p₄”, which is a simpleconcatenation of the K information bits (K=10) and the J CRC bits (J=4),may be input to the polar encoder. Here,“i₁,i₂,i₃,i₄,i₅,i₆,i₇,i₈,i₉,i₁₀” represents the information bits, and“p₁,p₂,p₃,p₄” represents the CRC bits. In FIG. 11, if an interleaver,i.e., Int=(1,2,4,11,7,8,9,13,5,6,12,3,14) is used, an input of“i₁i₂,i₄,p₁,i₇,i₈,i₉,p₃,i₅,i₆,p₂,i₃,p₄” may be input to the polarencoder. That is, when an interleaver is applied to a sequenceconsisting of information bits and CRC bits, the CRC bits may bedistributedly arranged. The present disclosure proposes a method ofdesigning an interleaver, and the bit interleaver according to thepresent disclosure may be implemented as follows.

Bit Interleaver

In the present disclosure, Int patterns are obtained by inputtingcandidate seed values to a bit interleaver algorithm according to thepresent disclosure, and among the obtained Int patterns, an optimal seedvalue(s) that generates an Int pattern(s) with the best performance iscalculated. In this case, a seed value that generates an interleavingpattern having good performance in terms of early termination of CALdecoding using distributed CRC may be selected as the optimal seedvalue. For example, according to the present disclosure, a seed valuethat minimizes the sum of position indices of a predetermined number ofparity bits in an interleaver pattern (a pattern consisting of theindices of interleaved bits), that is, places the predetermined numberof parity bits at the front side of the interleaver pattern may bedetermined as the optimal seed value. Input parameters of the bitinterleaver algorithm, candidate seed values, and output values thereofmay be represented as follows.

* Input: information bit size K, CRC bit size J, K*(K+J) CRC generatormatrix G = [I_(K)*_(K); P_(K)*_(J)], where I_(K)*_(K) is a K*K identitymatrix. * Seed value: s = (j₁, ..., j_(J)) (permutation of (1, ...,J)). * Output: A set of K+J interleaved indices Int

Here, the seed value s is a permutation of parity bit indices, i.e., CRCbit indices. For example, when the seed value s is (1, 3, 2, 4), whichis a permutation of CRC bit indices of (1, 2, 3, 4), the seed value smay change the order of CRC bits from “p₁,p₂,p₃,p₄” to “p₁,p₃,p₂,p₄”.

To calculate the seed value for the optimal interleaver pattern, theinterleaver pattern Int needs to be calculated for each candidate seedvalue. For example, the algorithm in Table 1 below may be used todetermine the positions of parity bits and information bits based on agiven seed value and CRC generator matrix. In other words, the algorithmbelow may be used to calculate a sequence of interleaved indices basedon a seed value and a CRC generator. Considering that a relationshipbetween the parity and information bits is determined by the CRCpolynomial (i.e., CRC generator matrix), a unique sequence ofinterleaved indices, i.e., a unique interleaving pattern may be obtainedby the following algorithm.

TABLE 1 * Initialization: S = [ ] // empty set u = 0 * Algorithm(Pseudocode): for j = 1 to J t = P_(K)*_(J)(:, s(j)) // s(j)-th columnof the matrix P_(K)*_(J) Φ = find(t) // Φ contains the indices ofnon-zero locations in t -- (1) ε = Φ \S // set difference Φ − S -- (2)for k = 1 to |ε| // |ε| denotes the number of elements in ε Int(u + k) =ε(k) -- (3) end Int(u + |ε| +k) = K + s(j) -- (4) u = u + length(ε) + 1S = S ∪ ε end

In Table 1, “:” of P_(K*J)(:, s(j)) denotes all rows, and thusP_(K*J)(:, s(j)) refers to an s(j)-th column of the matrix P_(K*J). Inaddition, s(j) denotes the value of an j-th element in a seed vector.For example, in the case of s=(1, 3, 2, 4), s(1), s(2), s(3), and s(4)denote 1, 3, 2, and 4, respectively. Equation (1) in Table 1 denotes theposition(s) of an input bit(s) used to generate a parity bit, that is,input bit(s) connected to the corresponding parity bit. In other words,Equation (1) calculates an information bit that needs to be placedbefore a selected parity bit. Equation (2) in Table 1 denotes theposition(s) of a new input bit(s) not included in a previous parity bit.In other words, Equation (2) calculates an information bit except bitsconnected to a parity bit(s) prior to a currently added parity bit(hereinafter referred to as a current parity bit) among information bitsthat need to be placed before the current parity bit. Since S denotesthe position(s) of an input bit(s) used to generate a previous paritybit(s) and c denotes the position(s) of an input bit(s) used to generatea new parity bit(s), the algorithm in Table 1 may be used for generatingparity bits using the previous parity bit(s) and the new input bit(s).Equation (3) in Table 1 represents the position of the new input bit ofEquation (2), and the new input bit needs to be placed before the addedparity bit. Equation (4) represents the position of the parity bitgenerated by Equation (2).

Hereinafter, Examples 1, 2, 3, and 4 will be described in detail forbetter understanding of the present disclosure.

EXAMPLE 1

In Example 1, a method of implementing a length-16 interleaver using thealgorithm proposed in the present disclosure when the number ofinformation bits K and the number of CRC bits J are 12 and 4,respectively, will be described.

* Input: K=12, J=4, s=(1,3,2,4), and G=[I_(12*12),P_(12*4)], whereP_(12*4) is shown in Equation 13 below. In this case, a generatorpolynomial used for a CRC code, i.e., a CRC polynomial is determined ineach communication system, and the generator matrix G is just adifferent name of the CRC polynomial. Thus, a unique party matrix isobtained from a given CRC polynomial.

$\begin{matrix}{P_{12 \times 4} = \begin{bmatrix}0 & 0 & 0 & 1 \\1 & 1 & 0 & 0 \\0 & 1 & 1 & 0 \\0 & 0 & 1 & 1 \\1 & 1 & 0 & 1 \\1 & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\1 & 1 & 1 & 0 \\0 & 1 & 1 & 1 \\1 & 1 & 1 & 1 \\1 & 0 & 1 & 1 \\1 & 0 & 0 & 1\end{bmatrix}} & {{Equation}\mspace{14mu} 13}\end{matrix}$

When the seed value s is (1, 3, 2, 4), “1”, “3”, “2”, and “4” representthe indices of columns in Equation 13. The seed value changes the columnorder of the parity matrix from (1, 2, 3, 4) to (1, 3, 2, 4).

Assuming that an i-th column of the matrix in Equation 13 is c_(i), c₁,c₂, c₃ and c₄ may be represented as follows:c₁=[0,1,0,0,1,1,0,1,0,1,1,1]^(T), c₂=[0,1,1,0,1,0,1,1,1,1,0,0]^(T),c₃=[0,0,1,1,0,1,0,1,1,1,1,0]^(T), and c₃=[1,0,0,1,1,0,1,1,1,1]^(T).

>For j=1:

>>t=c₁, S=[ ] and u=0.

>>The following results: Φ={2,5,6,8,10,11,12} and c={2,5,6,8,10,11,12}may be obtained from Equations (1) and (2) of Table 1. Since Φ containsthe indices of non-zero positions in a j-th column t of the paritymatrix P_(K*J), it may be seen that Φ={2,5,6,8,10,11,12} by consideringthe positions of “1” of c₁=[0,1,0,0,1,1,0,1,0,1,1,1]^(T). Since εcorresponds to a difference between Φ and S and S is initially an emptyset, it may be seen that ε=Φ={2,5,6,8,10,11,12}.

>>Since the number of elements of ε={2,5,6,8,10,11,12} is 7,Int(u+k)=ε(k) may be determined as follows using Equation (3) of Table 1for k=1 to 7.

Int(0+1)=Int(1)=ε(1)=2,

Int(0+2)=Int(2)=ε(2)=5,

Int(0+3)=Int(3)=ε(3)=6,

Int(0+4)=Int(4)=ε(4)=8,

Int(0+5)=Int(5)=ε(5)=10,

Int(0+6)=Int(6)=ε(6)=11,

Int(0+7)=Int(7)=ε(7)=12.

>>The following result: Int(u+|ε|+1)=K+s(j), i.e.,Int(0+7+1)=Int(8)=12+s(1) may be obtained from Equation (4) of Table 1.In this example, since the seed value s is (1,3,2,4), s(1)=1. Thus,Int(8)=13.

>For j=2:

>>t=c₃, S={2,5,6,8,10,11,12} and u=8. For j=2, t denotes an s(2)-thcolumn in Equation 13, i.e., the third column therein. Since S={ },ε={2,5,6,8,10,11,12}, and u=0 for j=1, it may be seen from the equationsbelow Equation (4) of Table 1 that the following relationships: S=S Uε={ }U {2,5,6,8,10,11,12}={2,5,6,8,10,11,12} and u=u+length(ε)+1=0+7+1=8are satisfied for j=2.

>>The following results: Φ={3,4,6,8,9,10,11} and ε={3,4,9} may beobtained from equations (1) and (2) of Table 1. For j=2, Φ includes theposition indices of “1” in c₃=[0,0,1,1,0,1,0,1,1,1,1,0]^(T). The resultof ε={3,4,9} may be obtained by excluding the elements ofS={2,5,6,8,10,11,12} from Φ={3,4,6,8,9,10,11}.

>>Since the number of elements of ε={3,4,9} is 3, Int(u+k)=ε(k) may bedetermined as follows using Equation (3) of Table 1 for k=1 to 3.

Int(8+1)=Int(9)=ε(1)=3,

Int(8+2)=Int(10)=ε(2)=4,

Int(8+3)=Int(11)=ε(3)=9.

>>The following result: Int(u+|ε|+1)=K+s(j), i.e.,Int(8+3+1)=Int(12)=12+s(2) may be obtained from Equation (4) of Table 1.In this example, since the seed value s is (1,3,2,4), s(2)=3. Thus,Int(12)=15.

>For j=3:

>>t=c₂, S={2,3,4,5,6,8,9,10,11,12} and u=12. For j=3, t denotes ans(3)-th column in Equation 13, i.e., the second column therein. SinceS={2,5,6,8,10,11,12}, ε={3,4,9}, and u=8 for j=2, it may be seen fromthe equations below Equation (4) of Table 1 that the followingrelationships: S=S U ε={2,5,6,8,10,11,12} U{3,4,9}={2,3,4,5,6,8,9,10,11,12} and u=u+length(ε)+1=8+3+1=12 aresatisfied for j=3.

>>The following results: Φ={2,3,5,7,8,9,10} and ε={7} may be obtainedfrom Equations (1) and (2) of Table 1. For j=2, 1 includes the positionindices of “1” in c₂=[0,1,1,0,1,0,1,1,1,1,0,0]^(T). The result of ε={7}may be obtained by excluding the elements of S={2,3,4,5,6,8,9,10,11,12}from Φ={2,3,5,7,8,9,10}.

>>Since the number of elements of ε={7} is 1, Int(u+k)=ε(k) may bedetermined as follows using Equation (3) of Table 1 for k=1.

Int(12+1)=Int(13)=ε(1)=7.

>>The following result: Int(u+|ε|+1)=K+s(j), i.e.,Int(12+1+1)=Int(14)=12+s(3) may be obtained from Equation (4) ofTable 1. In this example, since the seed value s is (1,3,2,4), s(3)=2.Thus, Int(14)=14.

>For j=4:

>>t=c₄, S={2,3,4,5,6,7,8,9,10,11,12}, and u=14. For j=4, t denotes ans(4)-th column in Equation 13, i.e., the fourth column therein. SinceS={2,3,4,5,6,8,9,10,11,12}, ε={7}, and u=12 for j=3, it may be seen fromthe equations below Equation (4) of Table 1 that the followingrelationships: S=S U ε={2,3,4,5,6,8,9,10,11,12} U{7}={2,3,4,5,6,7,8,9,10,11,12} and u=u+length(ε)+1=12+1+1=14 aresatisfied for j=4.

>>The following results: Φ={1,4,5,7,9,10,11,12} and ε={1} may beobtained from Equations (1) and (2) of Table 1. For j=3, Φ includes theposition indices of “1” in c₂=[0,1,1,0,1,0,1,1,1,1,0,0]^(T). The resultof ε={1} may be obtained by excluding the elements ofS={2,3,4,5,6,7,8,9,10,11,12} from Φ={1,4,5,7,9,10,11,12}.

>>Since the number of elements of ε={2} is 1, Int(u+k)=ε(k) may bedetermined as follows using Equation (3) of Table 1 for k=1.

Int(14+1)=Int(15)=ε=1.

>>The following result: Int(u+|ε|ε|+1)=K+s(j), i.e.,Int(14+1+1)=Int(16)=12+s(4) may be obtained from Equation (4) ofTable 1. In this example, since the seed value s is (1,3,2,4), s(4)=4.Thus, Int(16)=16.

An output sequence based on the algorithm of Table 1, i.e., a sequenceobtained by arranging numerals from Int(1) to Int(15) is defined asfollows: Int=(2,5,6,8,10,11,12,13,3,4,9,15,7,14,1,16). InInt=(2,5,6,8,10,11,12,13,3,4,9,15,7,14,1,16), indices greater than thenumber of information bits (K=12) represent the positions of parity bitsin a bit sequence interleaved by the bit interleaver. For example, inthe case of using Int=(2,5,6,8,10,11,12,13,3,4,9,15,7,14,1,16),information bits and parity bits {p₁p₂, p₃,p₄} are interleaved by thebit interleaver as follows:{i₂,i₅,i₆,i₈i₁₀,i₁₁,i₁₂,p₁,i₃,i₄,i₉,p₃,i₇,p₂,i₁,p₄}. The interleaved bitsequence {i₂,i₅,i₆,i₈i₁₀,i₁₁,i₁₂,p₁,i₃,i₄,i₉,p₃,i₇,p₂,i₁,p₄} may beinput to the polar encoder of FIG. 11. In this case, the earlytermination may be performed as follows during the CAL decoding process.

>1. The polar decoder decodes (i₂,i₅,i₆,i₈i₁₀,i₁₁,i₁₂,p₁) which is apart of the input bits of the polar code, and then performs CRC-CHECKtherefor. If CRC-CHECK for all L candidate information bit sequences in(i₂,i₅,i₆,i₈i₁₀,i₁₁,i₁₂,p₁) fails, the polar decoder declares an errorand stops the decoding.

>2. If the polar decoder does not stop the decoding during CRC-CHECK for(i₂,i₅,i₆,i₈i₁₀,i₁₁,i₁₂,p₁), the polar decoder additionally decodes(i3,i4,i9,p3). Then, the decoder performs CRC-CHECK for(i₂,i₅,i₆,i₈,i₁₀,i₁₁,i₁₂,p₁,i₃,i₄,i₉,p₃). If CRC-CHECK for all Lcandidate information bit sequences in(i₂,i₅,i₆,i₈,i₁₀,i₁₁,i₁₂,p₁,i₃,i₄,i₉,p₃) fails, the polar decoderdeclares an error and stops the decoding.

>3. If the polar decoder does not stop the decoding while performingCRC-CHECK for (i₂,i₅,i₆,i₈i₁₀,i₁₁,i₁₂,p₁i₃,i₄,i₉,p₃), the polar decoderadditionally decodes (i₇,p₂). Then, the decoder performs CRC-CHECK for(i₂,i₅,i₆,i₈,i₁₀,i₁₁,i₁₂,p₁,i₃,i₄,i₉,p₃,i₇,p₂). If CRC-CHECK for all Lcandidate information bit sequences in(i₂,i₅,i₆,i₈,i₁₀,i₁₁,i₁₂,p₁,i₃,i₄,i₉,p₃,i₇,p₂) fails, the polar decoderdeclares an error and stops the decoding.

>4. If the polar decoder does not stop the decoding while performingCRC-CHECK for (i₂,i₅,i₆,i₈,i₁₀,i₁₁,i₁₂,p₁,i₃,i₄,i₉,p₃,i₇,p₂), the polardecoder additionally decodes (i₁,p₄). Then, the decoder performsCRC-CHECK for (i₂,i₅,i₆,i₈,i₁₀,i₁₁,i₁₂,p₁,i₃,i₄,i₉,p₃,i₇,p₂i₁,p₄). IfCRC-CHECK for all L candidate information bit sequences in(i₂,i₅,i₆,i₈,i₁₀,i₁₁,i₁₂,p₁,i₃,i₄,i₉,p₃,i₇,p₂) fails, the polar decoderdeclares an error and stops the decoding. The polar decoder determines acandidate that passes CRC-CHECK among L candidate information bitsequences in (i₂,i₅,i₆,i₈,i₁₀,i₁₁,i₁₂,p₁,i₃,i₄,i₉,p₃,i₇,p₂i₁,p₄) as adecoded information bit sequence. If CRC-CHECK for all the candidatesfails, the polar decoder declares an error.

A generator polynomial used for generating a CRC code may be defined ineach communication system. A unique generator matrix G may be obtainedfrom a given generator polynomial, and thus a unique party matrix mayalso be determined based on the given generator polynomial. Even when aCRC generator polynomial different from the CRC generation polynomial ofG=[I_(12*12),P_(12*4)] described in the above example is used, aninterleaver pattern, i.e., a pattern of interleaved bit indices may beobtained by applying the above-described interleaver design principal(i.e., the algorithm of Table 1). When different CRC polynomials areused for uplink and downlink, different interleavers (i.e., differentinterleaving patterns) may be used for the same information size (i.e.,the same number of information bits). Since interleaving is appliedbefore information bits are input to the polar code, the sameinterleaver may be used even though the size of a mother polar code ischanged for the same information size.

EXAMPLE 2

In Example 2, interleavers for various information bit lengths, whichare designed based on the proposed algorithm, will be described. InExample 2, it is assumed that a 19-bit CRC code is used and thegenerator polynomial in Equation 14 below is used for the 19-bit CRCcode.

x¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1   Equation 14

* K=5, J=19

For K=5 and J=19, the seed value s for generating the optimalinterleaver pattern is as follows: s=(6, 7, 8, 4, 3, 10, 14, 16, 19, 18,15, 11, 12, 1, 5, 2, 9, 13, 17), and the interleaver pattern Intobtained from the optimal seed value is as follows: Int=(5, 11, 4, 12,13, 2, 3, 9, 1, 8, 15, 19, 21, 24, 23, 20, 16, 17, 6, 10, 7, 14, 18,22).

* K=13, J=19

For K=13 and J=19, the seed value s for generating the optimalinterleaver pattern is as follows: s=(5, 6, 9, 7, 19, 4, 11, 15, 18, 3,17, 14, 1, 12, 16, 2, 13, 10, 8), and the interleaver pattern Intobtained from the optimal seed value is as follows: Int=(4, 7, 8, 11,13, 18, 1, 3, 19, 6, 9, 22, 2, 12, 20, 32, 10, 17, 5, 24, 28, 31, 16,30, 27, 14, 25, 29, 15, 26, 23, 21).

* K=45, J=19

For K=45 and J=19, the seed value s for generating the optimalinterleaver pattern is as follows: s=(5, 8, 4, 15, 7, 19, 18, 16, 6, 14,10, 12, 13, 9, 11, 2, 1, 3, 17), and the interleaver pattern Intobtained from the optimal seed value is as follows: Int=(6, 7, 8, 10,11, 16, 18, 19, 20, 23, 26, 27, 28, 30, 32, 36, 39, 40, 43, 45, 50, 1,4, 13, 14, 24, 34, 37, 44, 53, 2, 9, 29, 42, 49, 5, 12, 15, 17, 21, 22,25, 33, 38, 41, 60, 3, 35, 52, 31, 64, 63, 61, 51, 59, 55, 57, 58, 54,56, 47, 46, 48, 62).

As another method, in the case of non-distributed CRC bits, since theearly termination of decoding guarantees no gain in spite ofinterleaving, the corresponding CRC bits may be arranged within aninterleaving pattern in the order of bit indices. For example, Int=(6,7, 8, 10, 11, 16, 18, 19, 20, 23, 26, 27, 28, 30, 32, 36, 39, 40, 43,45, 50, 1, 4, 13, 14, 24, 34, 37, 44, 53, 2, 9, 29, 42, 49, 5, 12, 15,17, 21, 22, 25, 33, 38, 41, 60, 3, 35, 52, 31, 64, 63, 61, 51, 59, 55,57, 58, 54, 56, 47, 46, 48, 62), since indices of (64, 63, 61, 51, 59,55, 57, 58, 54, 56, 47, 46, 48, 62), which are greater than 45, areconsecutively arranged, there is no effect on the early termination gaineven if the indices are arranged in the index order. Accordingly,Int=(6, 7, 8, 10, 11, 16, 18, 19, 20, 23, 26, 27, 28, 30, 32, 36, 39,40, 43, 45, 50, 1, 4, 13, 14, 24, 34, 37, 44, 53, 2, 9, 29, 42, 49, 5,12, 15, 17, 21, 22, 25, 33, 38, 41, 60, 3, 35, 52, 31, 46, 47, 48, 51,54, 55, 56, 57, 58, 59, 61, 62, 63, 64) and Int=(6, 7, 8, 10, 11, 16,18, 19, 20, 23, 26, 27, 28, 30, 32, 36, 39, 40, 43, 45, 50, 1, 4, 13,14, 24, 34, 37, 44, 53, 2, 9, 29, 42, 49, 5, 12, 15, 17, 21, 22, 25, 33,38, 41, 60, 3, 35, 52, 31, 64, 63, 61, 51, 59, 55, 57, 58, 54, 56, 47,46, 48, 62) may have the same performance in terms of the earlytermination of decoding. In the present disclosure, interleavingpatterns obtained by changing the order of consecutive CRC bit indicesin an interleaver pattern generated by a specific optimal seed value mayhave the same performance regarding the early termination of decoding.In the present disclosure, when there are consecutive CRC bit indices inan interleaver pattern obtained based on a specific optimal seed valueand a specific CRC generator matrix, an interleaver pattern obtained bychanging the consecutive CRC bit indices may also be used as theinterleaver pattern based on the specific seed value.

* K=109, J=19

For K=109 and J=19, the seed value s for generating the optimalinterleaver pattern is as follows: s=(11, 10, 1, 12, 13, 17, 19, 2, 6,4, 14, 16, 5, 3, 15, 8, 18, 7, 9), and the interleaver pattern Intobtained from the optimal seed value is as follows: Int=(1, 2, 4, 5, 8,11, 12, 14, 16, 17, 20, 22, 24, 26, 27, 28, 31, 32, 34, 41, 48, 49, 53,54, 57, 61, 62, 65, 67, 69, 71, 80, 82, 85, 86, 88, 89, 90, 91, 93, 95,96, 101, 102, 103, 105, 107, 108, 120, 3, 6, 15, 19, 29, 30, 35, 44, 47,51, 52, 55, 56, 72, 74, 75, 77, 78, 87, 94, 98, 99, 106, 109, 119, 7, 9,25, 33, 36, 42, 45, 50, 63, 70, 73, 76, 79, 92, 100, 110, 13, 18, 21,23, 58, 66, 68, 81, 83, 97, 104, 121, 10, 43, 59, 64, 84, 122, 38, 46,126, 40, 60, 128, 37, 111, 39, 115, 113, 123, 125, 114, 112, 124, 117,127, 116, 118).

As a further method, in the case of non-distributed CRC bits, since theearly termination of decoding guarantees no gain in spite ofinterleaving, the corresponding CRC bits may be arranged within aninterleaving pattern in the order of bit indices. For example, for K=109and J=19, the following interleaver pattern: Int=(1, 2, 4, 5, 8, 11, 12,14, 16, 17, 20, 22, 24, 26, 27, 28, 31, 32, 34, 41, 48, 49, 53, 54, 57,61, 62, 65, 67, 69, 71, 80, 82, 85, 86, 88, 89, 90, 91, 93, 95, 96, 101,102, 103, 105, 107, 108, 120, 3, 6, 15, 19, 29, 30, 35, 44, 47, 51, 52,55, 56, 72, 74, 75, 77, 78, 87, 94, 98, 99, 106, 109, 119, 7, 9, 25, 33,36, 42, 45, 50, 63, 70, 73, 76, 79, 92, 100, 110, 13, 18, 21, 23, 58,66, 68, 81, 83, 97, 104, 121, 10, 43, 59, 64, 84, 122, 38, 46, 126, 40,60, 128, 37, 111, 39, 112, 113, 114, 115, 116, 117, 118, 123, 124, 125,127) may be used. Further, in Int=(1, 2, 4, 5, 8, 11, 12, 14, 16, 17,20, 22, 24, 26, 27, 28, 31, 32, 34, 41, 48, 49, 53, 54, 57, 61, 62, 65,67, 69, 71, 80, 82, 85, 86, 88, 89, 90, 91, 93, 95, 96, 101, 102, 103,105, 107, 108, 120, 3, 6, 15, 19, 29, 30, 35, 44, 47, 51, 52, 55, 56,72, 74, 75, 77, 78, 87, 94, 98, 99, 106, 109, 119, 7, 9, 25, 33, 36, 42,45, 50, 63, 70, 73, 76, 79, 92, 100, 110, 13, 18, 21, 23, 58, 66, 68,81, 83, 97, 104, 121, 10, 43, 59, 64, 84, 122, 38, 46, 126, 40, 60, 128,37, 111, 39, 115, 113, 123, 125, 114, 112, 124, 117, 127, 116, 118),interleaver patterns obtained by changing the positions of consecutiveCRC bit indices of (112, 113, 114, 115, 116, 117, 118, 123, 124, 125,127) may be used for K=109 and J=19.

* K=173, J=19

For K=173 and J=19, the optimal interleaver pattern Int is as follows:Int=(2, 6, 8, 14, 16, 17, 18, 20, 21, 22, 23, 24, 25, 33, 39, 43, 44,45, 46, 48, 49, 52, 54, 55, 59, 63, 64, 72, 75, 76, 78, 79, 81, 87, 88,89, 92, 95, 96, 98, 100, 101, 102, 106, 108, 110, 111, 114, 116, 117,118, 121, 122, 126, 127, 128, 129, 130, 131, 132, 133, 134, 139, 140,142, 143, 146, 147, 148, 150, 151, 152, 153, 154, 159, 161, 162, 164,167, 168, 169, 170, 171, 173, 176, 3, 9, 11, 13, 26, 27, 28, 32, 34, 35,37, 56, 58, 66, 67, 71, 73, 82, 84, 86, 91, 94, 97, 99, 103, 104, 119,124, 144, 145, 160, 163, 179, 5, 19, 36, 42, 47, 51, 57, 62, 90, 105,109, 113, 120, 125, 135, 136, 137, 149, 155, 156, 157, 165, 172, 174, 4,7, 10, 15, 38, 41, 50, 53, 61, 65, 83, 107, 112, 115, 123, 138, 158,178, 29, 30, 60, 68, 69, 74, 93, 141, 181, 12, 31, 70, 77, 85, 166, 192,1, 40, 80, 175, 177, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189,190, 191).

*K=237, J=19

For K=237 and J=19, the optimal interleaver pattern Int is as follows:Int=(4, 5, 6, 7, 8, 13, 16, 18, 20, 21, 22, 24, 29, 30, 32, 41, 42, 43,45, 46, 47, 50, 51, 53, 55, 57, 59, 60, 62, 63, 64, 67, 72, 73, 75, 77,82, 85, 86, 87, 90, 91, 92, 96, 98, 99, 101, 103, 107, 109, 116, 119,120, 122, 123, 127, 128, 130, 131, 135, 137, 139, 142, 143, 146, 148,150, 151, 155, 158, 160, 161, 162, 163, 166, 167, 168, 172, 174, 178,182, 183, 186, 188, 190, 192, 193, 195, 197, 198, 206, 207, 208, 209,210, 211, 212, 215, 216, 217, 218, 223, 224, 225, 227, 228, 231, 232,237, 243, 2, 19, 23, 25, 26, 27, 31, 34, 36, 39, 49, 52, 61, 66, 70, 78,80, 81, 84, 88, 89, 97, 108, 110, 112, 113, 118, 136, 140, 145, 152,153, 156, 159, 164, 165, 170, 175, 180, 181, 185, 191, 194, 196, 203,204, 214, 226, 233, 234, 235, 240, 3, 11, 15, 37, 48, 65, 71, 74, 79,95, 102, 104, 105, 117, 124, 126, 129, 132, 133, 144, 154, 169, 176,177, 189, 199, 213, 219, 221, 229, 230, 236, 248, 9, 10, 17, 28, 35, 40,44, 54, 68, 69, 76, 100, 114, 115, 125, 134, 138, 141, 149, 157, 179,200, 202, 205, 220, 256, 33, 56, 58, 93, 94, 106, 171, 201, 246, 38,121, 184, 252, 1, 12, 14, 111, 222, 249, 83, 147, 251, 173, 245, 238,247, 239, 187, 241, 242, 244, 246, 250, 253, 254, 255).

EXAMPLE 3

In Example 3, optimal seed values having good performance in the earlytermination for various information bit lengths will be described.Assuming that a 19-bit CRC code is used as in Example 2, and moreparticularly, assuming that the bit length of a CRC code is 19 and theCRC generator polynomial of Equation 14 is used, the following seedvalues may be used to interleave the following bit sequences, each ofwhich consists of information bit sequence+CRC code, based on the sum K′of the number of information bits K and the number of CRC bits J.

TABLE 2 The number (K′) of information + CRC bits Seed vector (s) K′ =32 s = (5, 6, 9, 7, 19, 4, 11, 15, 18, 3, 17, 14, 1, 12, 16, 2, 13, 10,8) 32 < K′ = 64 s = (5, 8, 4, 15, 7, 19, 18, 16, 6, 14, 10, 12, 13, 9,11, 2, 1, 3, 17) 64 < K′ = 96 s = (10, 11, 16, 18, 1, 7, 9, 2, 15, 4,17, 8, 12, 14, 19, 5, 3, 13, 6) 96 < K′ = 128 s = (11, 10, 1, 12, 13,17, 19, 2, 6, 4, 14, 16, 5, 3, 15, 8, 18, 7, 9) 128 < K′ = 160 s = (3,6, 12, 8, 17, 16, 11, 14, 19, 7, 9, 13, 4, 18, 2, 1, 10, 15, 5) 160 < K′= 192 s = (3, 6, 1, 5, 8, 19, 10, 2, 15, 4, 12, 11, 9, 17, 16, 13, 14,7, 18) 192 < K′ = 224 s = (11, 1, 8, 5, 18, 14, 7, 19, 3, 12, 16, 17, 6,13, 10, 9, 2, 4, 15) 224 < K′ s = (6, 3, 11, 19, 9, 15, 12, 14, 8, 1,10, 2, 17, 7, 13, 5, 18, 4, 16)

In Table 2, an interleaving pattern for K′=32, i.e., K=13 may be equalto the interleaving pattern for K=13 and J=19 described in Example 2. Aninterleaving pattern for K′=64, i.e., K=45 may be equal to theinterleaving pattern for K=54 and J=19 described in Example 2. Aninterleaving pattern for K′=128, i.e., K=109 may be equal to theinterleaving pattern for K=109 and J=19 described in Example 2. Aninterleaving pattern for K′=192, i.e., K=173 may be equal to theinterleaving pattern for K=173 and J=19 described in Example 2.

EXAMPLE 4

In Example 4, the granularity of K′ is set to 64 for optimal seed valueshaving good performance in the early termination, in contrast to Table 2in Example 3 which shows seed vectors by setting the granularity of K′to 32 for various information bit lengths. Assuming that a 19-bit CRCcode is used as in Example 2, and more particularly, assuming that thebit length of a CRC code is 19 and the CRC generator polynomial ofEquation 14 is used, the following seed values may be used to interleavethe following bit sequences, each of which consists of information bitsequence+CRC code, based on the sum K′ of the number of information bitsK and the number of CRC bits J.

TABLE 3 The number (K′) of information + CRC bits Seed vector (s) K′ =64 s = (5, 8, 4, 15, 7, 19, 18, 16, 6, 14, 10, 12, 13, 9, 11, 2, 1, 3,17) 64 < K′ = 128 s = (11, 10, 1, 12, 13, 17, 19, 2, 6, 4, 14, 16, 5, 3,15, 8, 18, 7, 9) 128 < K′ = 192 s = (3, 6, 1, 5, 8, 19, 10, 2, 15, 4,12, 11, 9, 17, 16, 13, 14, 7, 18) 192 < K′ = 256 s = (6, 3, 11, 19, 9,15, 12, 14, 8, 1, 10, 2, 17, 7, 13, 5, 18, 4, 16) 256 < K′ = 320 s = (3,6, 11, 13, 2, 8, 18, 4, 1, 12, 5, 7, 14, 17, 10, 15, 16, 19, 9) 320 < K′= 384 s = (6, 3, 11, 5, 1, 8, 2, 9, 17, 19, 15, 13, 14, 12, 18, 4, 10,16, 7) 384 < K′ = 448 s = (6, 3, 18, 2, 1, 16, 10, 19, 8, 17, 9, 13, 5,7, 4, 12, 14, 11, 15) 448 < K′ = 512 s = (3, 6, 11, 2, 5, 12, 16, 8, 10,1, 13, 17, 9, 19, 18, 7, 14, 15, 4) 512 < K′ = 576 s = (6, 11, 9, 7, 10,13, 16, 2, 8, 15, 4, 1, 3, 17, 19, 12, 5, 14, 18) 576 < K′ = 640 s = (1,2, 19, 8, 18, 16, 17, 13, 4, 12, 3, 7, 9, 6, 10, 5, 15, 11, 14) 640 < K′= 704 s = (19, 1, 18, 15, 16, 17, 6, 11, 2, 12, 9, 5, 7, 13, 4, 14, 10,8, 3) 704 < K′ = 768 s = (2, 1, 3, 12, 5, 4, 18, 15, 7, 16, 14, 13, 17,8, 6, 19, 10, 9, 11) 768 < K′ s = (1, 6, 9, 12, 13, 8, 10, 19, 14, 4,16, 5, 3, 2, 15, 7, 11, 17, 18)

In Table 3, an interleaving pattern for K′=64, i.e., K=45 may be equalto the interleaving pattern for K=54 and J=19 described in Example 2. Aninterleaving pattern for K′=128, i.e., K=109 may be equal to theinterleaving pattern for K=109 and J=19 described in Example 2. Aninterleaving pattern for K′=192, i.e., K=173 may be equal to theinterleaving pattern for K=173 and J=19 described in Example 2. Aninterleaving pattern for K′=256, i.e., K=257 may be equal to theinterleaving pattern for K=237 and J=19 described in Example 2.

In Examples 3 and 4, K′ denotes a bit length including the number of CRCbits, that is, the sum of the information bit size and the CRC bit size.For a specific seed value (or seed vector) and a specific CRC generatorpolynomial, a unique interleaving (or interleaver) pattern is determinedbased on the number of information bits and the number of CRC bits.Thus, a seed value in Table 2 of Example 3 or Table 3 of Example 4 mayrepresent an interleaver pattern for each value of K′ based on the19-bit CRC code and the CRC generator polynomial of Equation 14. Inparticular, Table 2 of Example 3 and Table 3 of Example 4 showsinterleaving patterns for the individual ranges of multiple K′ values.For example, referring to Table 3, when K′=50, an encoder and decoderaccording to the present disclosure may modify and use an interleavingpattern when K′=64. When K′=K_(max)−k (where K_(max) is the maximumvalue among K′ values in a range to which K′ belongs), if idx(K_(max))represents index values of an interleaving pattern for K_(max), indexvalues of an interleaving pattern for K′ may be obtained by selectingvalues greater than 0 among values of idx(K_(max))−1. In other words,when K′=K_(max)−k, the indices of the interleaving pattern for K′ may beobtained by selecting values greater than 0 among values obtained bysubtracting k from each of the indices of the interleaving pattern forK_(max). For example, when K_(max)=6 and the indices of a correspondinginterleaver pattern are {1,3,2,5,4,6}, an interleaver pattern for K′=4is {1,3,2,4}, which is obtained by selecting values greater than 0 among{4,1,0,3,2,4}. Alternatively, an interleaver pattern composed of thefollowing values may be used as the interleaver pattern for K′. First,index values are obtained by excluding index values greater than K′ fromthe reverse values (K_(max)−idx(K_(max))+1) of the index values of theinterleaver pattern for K_(max), and then the obtained index values arereversed again with respect to K′ again (=K′−idx(K′)+1). Using thesevalues, the above interleaver pattern is configured. For example, whenK_(max)=6 and the indices of a corresponding interleaver pattern is{1,3,2,5,4,6}, an interleaver pattern for K′=4 is {1,3,2,4}. Theinterleaver pattern for K′=4 is obtained as follows. Indices of{6,4,5,2,3,1} are obtained by reversing the interleaver pattern forK_(max)=6, {1,3,2,5,4,6}, indices of {4,2,3,1} are obtained bydiscarding indices greater than K′=4, and then the interleaver patternfor K′=4, {1,3,2,4} is obtained by reversing each of the indices of{4,2,3,1} with respect to 4.

According to the present disclosure, the number of distributed CRC bitsmay vary depending on the granularity of K′ (the granularity is set to32 in Table 2 and 64 in Table 3). For example, for the same value of K′,seed vectors when the granularity of K′ is 32 may be different fromthose when the granularity of K′ is 54 as shown in Tables 2 and 3. Inaddition, according to the present disclosure, even if the granularityof K′ is the same, the number of distributed CRC bits may vary dependingon mother code sizes, coding rates, or K′ values. For example, in Tables2 and 3, a seed vector to be used may be determined for each range of K′or for each value of K′.

FIG. 12 is a block diagram illustrating elements of a transmittingdevice 10 and a receiving device 20 for implementing the presentdisclosure.

The transmitting device 10 and the receiving device 20 respectivelyinclude radio frequency (RF) units 13 and 23 capable of transmitting andreceiving radio signals carrying information, data, signals, and/ormessages, memories 12 and 22 for storing information related tocommunication in a wireless communication system, and processors 11 and21 operationally connected to elements such as the RF units 13 and 23and the memories 12 and 22 to control the elements and configured tocontrol the memories 12 and 22 and/or the RF units 13 and 23 so that acorresponding device may perform at least one of the above-describedexamples of the present disclosure.

The memories 12 and 22 may store programs for processing and controllingthe processors 11 and 21 and may temporarily store input/outputinformation. The memories 12 and 22 may be used as buffers.

The processors 11 and 21 generally control the overall operation ofvarious modules in the transmitting device and the receiving device.Especially, the processors 11 and 21 may perform various controlfunctions to implement the present disclosure. The processors 11 and 21may be referred to as controllers, microcontrollers, microprocessors, ormicrocomputers. The processors 11 and 21 may be implemented by hardware,firmware, software, or a combination thereof. In a hardwareconfiguration, application specific integrated circuits (ASICs), digitalsignal processors (DSPs), digital signal processing devices (DSPDs),programmable logic devices (PLDs), or field programmable gate arrays(FPGAs) may be included in the processors 11 and 21. Meanwhile, if thepresent disclosure is implemented using firmware or software, thefirmware or software may be configured to include modules, procedures,functions, etc. performing the functions or operations of the presentdisclosure. Firmware or software configured to perform the presentdisclosure may be included in the processors 11 and 21 or stored in thememories 12 and 22 so as to be driven by the processors 11 and 21.

The processor 11 of the transmitting device 10 performs predeterminedcoding and modulation for a signal and/or data scheduled to betransmitted to the outside by the processor 11 or a scheduler connectedwith the processor 11, and then transfers the coded and modulated datato the RF unit 13. For example, the processor 11 converts a data streamto be transmitted into K layers through demultiplexing, channel coding,scrambling, and modulation. The coded data stream is also referred to asa codeword and is equivalent to a transport block which is a data blockprovided by a MAC layer. One transport block (TB) is coded into onecodeword and each codeword is transmitted to the receiving device in theform of one or more layers. For frequency up-conversion, the RF unit 13may include an oscillator. The RF unit 13 may include N_(t) (where N_(t)is a positive integer) transmit antennas.

A signal processing process of the receiving device 20 is the reverse ofthe signal processing process of the transmitting device 10. Undercontrol of the processor 21, the RF unit 23 of the receiving device 20receives radio signals transmitted by the transmitting device 10. The RFunit 23 may include N_(r) (where N_(r) is a positive integer) receiveantennas and frequency down-converts each signal received throughreceive antennas into a baseband signal. The processor 21 decodes anddemodulates the radio signals received through the receive antennas andrestores data that the transmitting device 10 intended to transmit.

The RF units 13 and 23 include one or more antennas. An antenna performsa function for transmitting signals processed by the RF units 13 and 23to the exterior or receiving radio signals from the exterior to transferthe radio signals to the RF units 13 and 23. The antenna may also becalled an antenna port. Each antenna may correspond to one physicalantenna or may be configured by a combination of more than one physicalantenna element. The signal transmitted from each antenna cannot befurther deconstructed by the receiving device 20. An RS transmittedthrough a corresponding antenna defines an antenna from the view pointof the receiving device 20 and enables the receiving device 20 to derivechannel estimation for the antenna, irrespective of whether the channelrepresents a single radio channel from one physical antenna or acomposite channel from a plurality of physical antenna elementsincluding the antenna. That is, an antenna is defined such that achannel carrying a symbol of the antenna can be obtained from a channelcarrying another symbol of the same antenna. An RF unit supporting aMIMO function of transmitting and receiving data using a plurality ofantennas may be connected to two or more antennas.

The transmitting device 10 may include an interleaver and a polarencoder according to the present disclosure, and the receiving device 20may include an interleaving pattern and a polar decoder according to thepresent disclosure. For example, the processor 11 of the transmittingdevice 10 may be configured to interleave a CRC-encoded bit sequenceconsisting of information bits and distributed CRC bits using theinterleaving pattern according to the present disclosure. The processor11 of the transmitting device 10 may be configured to perform polarencoding of the interleaved bit sequence. The processor 11 of thetransmitting device 10 may be configured to control the transceiver 13to transmit bits encoded using a polar code. The processor 21 of thereceiving device 20 may be configured to control the transceiver 23 ofthe receiving device 20 to receive a radio signal containing encodedbits from the transmitting device 10. The processor 21 of the receivingdevice 20 may be configured to perform polar decoding of the receivingsignal. For example, the processor 21 of the receiving device 20 may beconfigured to decode an information bit(s) and distributed CRC bitsconcatenated with the information bit(s) and perform CRC-CHECK therefor,using the interleaving pattern according to the present disclosure. Theinterleaver and polar encoder based on the interleaving patternaccording to the present disclosure may be implemented as a part of theprocessor 11 of the transmitting device 10, and the polar decoderaccording to the present disclosure may be implemented as a part of theprocessor 21 of the receiving device 20. The processor 11 of thetransmitting device 10 may be configured to control the interleaver, thepolar encoder, and a CRC encoder configured to perform CRC encoding. Theprocessor 21 of the receiving device 20 may be configured to control thepolar decoder and a CRC decoder according to the interleaving patternused by the transmitting device 10 or the interleaving patterncorresponding to the interleaver.

As described above, the detailed description of the preferredimplementation examples of the present disclosure has been given toenable those skilled in the art to implement and practice thedisclosure. Although the disclosure has been described with reference toexemplary examples, those skilled in the art will appreciate thatvarious modifications and variations can be made in the presentdisclosure without departing from the spirit or scope of the disclosuredescribed in the appended claims. Accordingly, the disclosure should notbe limited to the specific examples described herein, but should beaccorded the broadest scope consistent with the principles and novelfeatures disclosed herein.

Examples of the present disclosure may be used for a processing chipconnected to or mounted in a BS, a UE, or a communication device in awireless communication system, or for other equipment.

What is claimed is:
 1. A method of transmitting information by atransmitting device in a wireless communication system, the methodcomprising: generating K+J bits by adding J cyclic redundancy check(CRC) bits to K information bits; interleaving the K+J bits according toan interleaving pattern based on a seed value for permuting the J CRCbits; encoding the interleaved bits based on a polar code; andtransmitting the encoded bits to a receiving device, wherein the seedvalue is predetermined based on K.
 2. The method of claim 1, wherein,based on J=19 and a CRC generator polynomial ofx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1 for generation of theJ CRC bits, a seed value for K+J=64 iss=(5,8,4,15,7,19,18,16,6,14,10,12,13,9,11,2,1,3,17).
 3. The method ofclaim 2, wherein an interleaving pattern for K+J=64 is Int=(6, 7, 8, 10,11, 16, 18, 19, 20, 23, 26, 27, 28, 30, 32, 36, 39, 40, 43, 45, 50, 1,4, 13, 14, 24, 34, 37, 44, 53, 2, 9, 29, 42, 49, 5, 12, 15, 17, 21, 22,25, 33, 38, 41, 60, 3, 35, 52, 31, 64, 63, 61, 51, 59, 55, 57, 58, 54,56, 47, 46, 48, 62).
 4. The method of claim 3, wherein an interleavingpattern for K+J=K′ smaller than 64 includes values greater than 0 amongvalues obtained by subtracting 64−K from each element of theinterleaving pattern for K+J=64.
 5. The method of claim 1, wherein basedon J=19 and a CRC generator polynomial ofx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1 for generation of theJ CRC bits, a seed value for K+J=128 iss=(11,10,1,12,13,17,19,2,6,4,14,16,5,3,15,8,18,7,9).
 6. The method ofclaim 1, wherein based on J=19 and a CRC generator polynomial ofx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1 for generation of theJ CRC bits, a seed value for K+J=192 iss=(3,6,1,5,8,19,10,2,15,4,12,11,9,17,16,13,14,7,18).
 7. The method ofclaim 1, wherein based on J=19 and a CRC generator polynomial ofx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1 for the J CRC codes,a seed value for K+J=256 iss=(6,3,11,19,9,15,12,14,8,1,10,2,17,7,13,5,18,4,16).
 8. The method ofclaim 1, wherein based on J=19 and a CRC generator polynomial ofx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1 for the J CRC codes,a seed value for K+J=320 iss=(3,6,11,13,2,8,18,4,1,12,5,7,14,17,10,15,16,19,9).
 9. The method ofclaim 1, wherein based on J=19 and a CRC generator polynomial ofx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1 for the J CRC codes,a seed value for K+J=384 iss=(6,3,11,5,1,8,2,9,17,19,15,13,14,12,18,4,10,16,7).
 10. The method ofclaim 1, wherein based on J=19 and a CRC generator polynomial ofx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1 for the J CRC codes,a seed value for K+J=448 iss=(6,3,18,2,1,16,10,19,8,17,9,13,5,7,4,12,14,11,15).
 11. The method ofclaim 1, wherein based on J=19 and a CRC generator polynomial ofx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1 for the J CRC codes,a seed value for K+J=512 iss=(3,6,11,2,5,12,16,8,10,1,13,17,9,19,18,7,14,15,4).
 12. The method ofclaim 1, wherein based on J=19 and a CRC generator polynomial ofx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1 for the J CRC codes,a seed value for K+J=576 iss=(6,11,9,7,10,13,16,2,8,15,4,1,3,17,19,12,5,14,18).
 13. The method ofclaim 1, wherein based on J=19 and a CRC generator polynomial ofx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1 for the J CRC codes,a seed value for K+J=640 iss=(1,2,19,8,18,16,17,13,4,12,3,7,9,6,10,5,15,11,14).
 14. The method ofclaim 1, wherein based on J=19 and a CRC generator polynomial ofx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1 for the J CRC codes,a seed value for K+J=704 iss=(19,1,18,15,16,17,6,11,2,12,9,5,7,13,4,14,10,8,3).
 15. The method ofclaim 1, wherein based on J=19 and a CRC generator polynomial ofx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1 for the J CRC codes,a seed value for K+J=768 iss=(2,1,3,12,5,4,18,15,7,16,14,13,17,8,6,19,10,9,11).
 16. The method ofclaim 1, wherein based on J=19 and a CRC generator polynomial ofx¹⁹+x¹⁸+x¹⁶+x¹⁵+x¹⁴+x¹³+x¹²+x¹⁰+x⁹+x⁷+x⁵+x³+x²+x+1 for the J CRC codes,a seed value for K+J>768 iss=(1,6,9,12,13,8,10,19,14,4,16,5,3,2,15,7,11,17,18).
 17. A transmittingdevice for transmitting information in a wireless communication system,the transmitting device comprising: a cyclic redundancy check (CRC)encoder configured to generate K+J bits by adding J CRC bits to Kinformation bits; an interleaver configured to interleave the K+J bitsaccording to an interleaving pattern based on a seed value for permutingthe J CRC bits; a polar encoder configured to encode the interleavedbits based on a polar code; and a transceiver configured to transmit theencoded bits to a receiving device, wherein the seed value ispredetermined based on K.
 18. A method of receiving information by areceiving device in a wireless communication system, the methodcomprising: receiving, from a transmitting device, K+J bits encodedbased on a polar code, wherein K is a number of information bits and Jis a number of cyclic redundancy check (CRC) bits; and decoding the K+Jbits based on the polar code according to an interleaving pattern,wherein the interleaving pattern is based on a seed value for permutingthe J CRC bits, and wherein the seed value is predetermined based on K.19. A receiving device for receiving information in a wirelesscommunication system, the receiving device comprising: a transceiverconfigured to receive, from a transmitting device, K+J bits encodedbased on a polar code, wherein K is a number of information bits and Jis a number of cyclic redundancy check (CRC) bits; and a polar decoderconfigured to decode the K+J bits based on the polar code according toan interleaving pattern, wherein the interleaving pattern is based on aseed value for permuting the J CRC bits, and wherein the seed value ispredetermined based on K.